Integrated topology control and routing in wireless optical mesh networks

Computer Networks 51 (2007) 4237–4251

www.elsevier.com/locate/comnet

Integrated topology control and routing in wireless opticalmesh networks q

Abhishek Kashyap a,*, Kwangil Lee a, Mehdi Kalantari a, Samir Khuller b,Mark Shayman a

a Department of Electrical and Computer Engineering, University of Maryland, College Park, United Statesb Department of Computer Science, University of Maryland, College Park, United States

Received 18 March 2006; received in revised form 15 March 2007; accepted 21 May 2007Available online 8 June 2007

Responsible Editor: A. Fumagalli

Abstract

We study the problem of integrated topology control and routing in Free Space Optical (FSO) mesh backbone net-works. FSO links are high-bandwidth, low interference links that can be set-up very fast, making them suitable for meshnetworking. FSO networks are highly constrained by interface constraints, i.e., constraints on the number of FSO links anode can establish. We prove the problem to be NP-Hard and propose efficient algorithms for integrated topology controland single-path or multi-path routing.� 2007 Elsevier B.V. All rights reserved.

Keywords: Wireless mesh networks; Free space optical networks; Topology control and routing; Rollout algorithms; Matching; Multi-commodity flow

1. Introduction

Wireless mesh networks have gained much popu-larity due to their application in last mile extensionof metropolitan area networks (MANs), and localarea networks (LANs). In last mile extensions of

1389-1286/$ - see front matter � 2007 Elsevier B.V. All rights reserved

doi:10.1016/j.comnet.2007.05.006

q This research was partially supported by AFOSR under grantF496200210217 and NSF under grant CNS-0435206.

* Corresponding author. Tel.: +1 301 405 5711.E-mail addresses: [email protected] (A. Kashyap),

[email protected] (K. Lee), [email protected] (M.Kalantari), [email protected] (S. Khuller), [email protected] (M. Shayman).

MANs, wireless mesh networks are multi-hop net-works being used as backbone networks connectingend-users (LAN gateways connected to mesh routersin the network) with the access points connected tothe Internet. Wireless mesh networks are an attrac-tive option over optical fibers because of their easeof installation and cost-effectiveness of deployment.

Various technologies have been proposed for usein wireless mesh networks: 802.15 (UWB) [1] is pro-posed for personal area mesh networks, 802.11 s[22] is proposed for local area mesh networking,and 802.16 (WiMax) [2] is proposed for MANs (lastmile extension). All the proposed standards assumea shared physical channel and use RF technology,

.

mailto:[email protected]




mailto:shayman@glue.

4238 A. Kashyap et al. / Computer Networks 51 (2007) 4237–4251

which is prone to interference among transmittersand provides low security [5]. Also, a node fartherfrom an access point may get a much lowerthroughput (compared to nodes closer to the accesspoint, resulting in unfairness) using currentlydeployed MAC and routing protocols [19]. Thus,the throughput, end-to-end delay and fairnessdegrade as the number of nodes or number of hopsincreases. Therefore the RF-based technologiesusing current protocols are not scalable with thenetwork size [5]. Generally, it is desired to providebandwidth guarantees and QoS to traffic on wirelessmesh backbone networks, as in IP networks. Thus,due to aforementioned reasons, RF-based technolo-gies are not completely suitable to be deployed inwireless mesh backbone networks.

Free Space Optics (FSO) [40] technology is anattractive option for use in mesh networks [44].FSO links are point-to-point links that use long-range (up to 4 km in current products), high band-width (up to 2.5 Gbps in current products) narrowlaser beams. There is very low interference amongtransmitters, and difficulty in intercepting the verynarrow laser beam provides high security. There-fore, the technology is scalable with the number ofnodes and number of hops in the network andFSO links can provide the QoS required by theend-users. Also, FSO links offer the flexibility of fasttracking and setup of links [23]. Thus, the networktopology can be reconfigured very easily as the traf-fic pattern or node positions change. These attrac-tive characteristics of FSO links make themsuitable for use in military backbones networks aswell. FSO links have the problem of obscurationdue to atmospheric conditions such as fog andsnow. This problem can be alleviated by usinghybrid RF/FSO networks, in which RF links areused for back-up in the event of FSO link obscura-tion [24,30,29]. The algorithms for hybrid RF/FSOnetworks can be used to route back-up traffic (andoptimize RF topology is RF interfaces are separate[29]) for the FSO topology and routing computedby algorithms proposed in this paper.

The number of FSO transceivers at a node is lim-ited due to cost concerns, and the selection of linksto be established at each node is very critical as thataffects the performance of the network. We call thisproblem topology control. In this paper, we proposealgorithms for establishing network topologies thatachieve good performance (our performance mea-sure is the throughput) for a given traffic profile.The traffic profile (expected aggregate demands)

within a domain can either be predicted by observ-ing the traffic in the network [16,15,9,37], or can beinferred from the Service Level Agreements (SLAs).It has been shown that the traffic profile in IP back-bone has a pseudo-periodic behavior on differenttime-scales (e.g., day, week, etc.), which is predict-able based on the past history of the traffic [16,17].We can exercise topology control based on theseprofiles to achieve better network performance.

There are important differences between topol-ogy control for reconfigurable wireline optical net-works and topology control for FSO networks. Inthe wireline case, transmission range (lightpathlength) is not a major issue. Furthermore, if theoptical layer has sufficient resources such that therouting and wavelength assignment problem isalways solvable, then whenever a source and desti-nation both have available interfaces, a direct con-nection (one logical hop) can be established. Incontrast, in the wireless case, unless the destinationis within the transmission range of the source, amultihop connection is required. Most algorithmsproposed for topology control for reconfigurablewireline optical networks use the fact that a directlightpath can be established between any two nodes[34,6,39,33,45], and hence are not applicable to ourproblem. The other algorithms are based on simu-lated annealing and genetic programming, whichare too slow (they have exponential time complex-ity) to be run periodically.

Leonardi et al. [34] give a detailed survey of theexisting approaches proposed for logical networkdesign in wireline optical networks. They groupthe heuristics into three categories of interest:

1. Mixed ILP formulation of the problem and usingheuristics for solving it suboptimally: The heuris-tics include simulated annealing and geneticprogramming, variable depth local search tech-niques, and LP relaxation and rounding. Thesemethods are very time intensive.

2. Maximization of single hop traffic flows: This setof heuristics [6,39,33,45] tries to maximize thethroughput by setting up direct lightpathsbetween sources and destinations having highertraffic demands. Thus, this set of heuristics isnot directly applicable to our case as we cannothave a single hop path between each source anddestination; we propose a heuristic derived fromthese in this paper, and show that the rolloutalgorithms are guaranteed to work better thanthat heuristic.

A. Kashyap et al. / Computer Networks 51 (2007) 4237–4251 4239

3. Heuristic maximization of single and multi-hoptraffic flows: [34] divides these into two catego-ries, one based on adding links to a null topologyand another based on removing links from a fulltopology. These heuristics extensively use the factthat a direct lightpath can be created between anytwo nodes, and thus are not applicable to ourproblem.

4. Another set of heuristics works on optimizingnode placement, which is not the problem weare considering here. We assume we cannot con-trol the placement of nodes.

The paper is organized as follows: Section 2 pre-sents the related work. Section 3 presents the net-work model and problem statement. Section 4describes the integrated topology control and sin-gle-path routing framework. Section 5 describesrollout algorithms for topology control and single-path routing, along with the simulation results. Sec-tion 6 gives the algorithms for topology control andmulti-path routing, with the simulation results. Sec-tion 7 discusses the computational complexity of thealgorithms. Section 8 concludes the paper.

2. Related work

There has been recent work on routing in wirelessoptical (or Free Space Optical (FSO)) networks [38].The authors assume a network model in which eachnode can transmit to a certain sector of angle a andradius r around it, and any node in that sector canhear it. This leads to multiple uni-directional linksfrom each node, depending on the number of receiv-ing nodes within its transmission sector. The networkis a sensor network, and the nodes communicate witha base station through multi-hop paths using theabove-described uni-directional links. The authorsprovide efficient algorithms for node discovery andpath computation in this network model. We assumea model in which one FSO transmitter can transmitto only one receiver at any point in time, and a recei-ver can receive from only one transmitter at a time;and there is a limitation on the number of transmit-ters and receivers at each node. Thus, there cannotbe an arbitrary number of uni-directional links froma single node. We also consider multiple ingress/egress nodes rather than having a single base station.We also consider the joint problem of topology con-trol (deciding which transmitter should align withwhich receiver) and routing. Thus, our problem isvery different from their problem.

There has also been recent work on topologycontrol in FSO networks [21]. The authors considera model as ours, in which there are a limited numberof transmitters and receivers at each node, and forthe transmitter needs to be aligned with the receiverfor communication. The authors propose algo-rithms for constructing a topology that is shownto be strongly connected for most instances of theproblem (it cannot be guaranteed for all values oflimit on transmitter/receiver to be connected sincethat problem is NP-hard).

There have been recent studies on topology con-trol in wireless optical networks: the problem oftopology control and multi-path routing for maxi-mizing throughput for a given traffic profile has beenconsidered in [27]. The problem of topology controland single-path routing for maximizing throughputhas been studied in [26]. The constraints are on thenumber of transceivers at each node, and on thecapacity of each link. The current paper integratesand expands on the results presented in [27,26]. Theproblem of maximizing throughput with the assump-tion of infinite amount of traffic to be sent betweenevery ingress–egress pair has been considered in [25].

A specific instance of the topology control androuting problem has been addressed in [13], thatassumes two transceivers per node, and establishesring topologies. The problem is NP-hard, and thusthey provide heuristics that are shown to generatea connected ring topology in most instances. Theobjective is to minimize congestion in the networkfor the given traffic matrix. Another specificinstance of the problem has been addressed in [12],with each node having three transceivers. Theauthors provide heuristics to design bi-connectednetworks with minimum congestion for a given traf-fic matrix. The authors provide cross-layer algo-rithms for topology control (without routing) in[35]. The algorithms weight each link according tothe Bit Error Rate (BER) with the objective to com-pute a minimum weight bi-connected topology forthe two specific cases of two and three transceiversper node. In another work [46], the two objectivesof minimizing the total BER and minimizing thecongestion in the network is considered and heuris-tics are provided to solve the multi-objective prob-lem. Our algorithms do not assume any suchrestriction on the number of transceivers per node.

We now mention some related work in the areaof routing and topology control for hybrid RF/FSO networks. Izadpanah et al. [24] propose theuse of monitoring average recent Bit Error Rates

1 Multi-hop routing has been shown to outperform single-hoprouting in FSO networks (where all nodes can potentially connectto all other nodes) [4], thus, the realistic restriction of havingmultiple hops actually improves the routing performance.

2 There has been work that enables bi-directional links as well[41,3]. Our algorithms will work in this scenario as well, althoughwith changes in the shortest path computation algorithms [31].


at each FSO link, and switching partial traffic to theparallel RF link if the value is below a threshold.They provide with decision steps for when to switchand how much traffic to switch. The authors alsopropose routing on shortest paths with the BERsrepresenting the link weights. The problem ofjointly optimizing RF and FSO routes to providemin–max weighted back-up guarantees has beenstudied in [30]. The traffic between each source–des-tination pair (traffic demand) is weighted accordingto percentage real-time traffic in it, and the objectiveis to maximize the minimum weighted fraction ofeach traffic demand that has back-up on RF links.The secondary objective is to maximize the through-put on remaining (FSO + RF) capacity of the net-work. The traffic and its back-up on RF linksflows simultaneously so immediate back-up can beprovided in the event of obscuration. The authorsalso propose algorithms for joint topology controland routing for RF links for given routing on theFSO network [29]. The network is assumed to bedivided into grids, and it is assumed a single grid(thus all links passing through it) is obscured at atime. Their is a probability associated with theobscuration of each grid, and the RF topologyand back-up routes are computed so as the maxi-mize the average (over grid failures) of the minimumback-up provided among traffic demands for eachgrid failure. The above-mentioned algorithms canbe used after design of topology and routing inthe FSO network using the algorithms presentedin the current paper.

3. Network model and problem statement

We model the network as a graph G = (V,E),where V is the set of nodes and E is the set of poten-tial links between them. A potential link existsbetween two vertices if they are within each other’stransmission range. We consider wireless backbonenetworks in which each wireless node is equippedwith point-to-point wireless optical interfaces. Theterminal nodes (users) may connect to the backbonenodes using omni-directional RF links. By the term‘node’ we implicitly mean ‘‘backbone node’’. Weassume that a node can transmit to another nodewithin its transmission range by aligning its trans-mitter with the other node’s receiver. The steeringof the optical beam can be performed in a varietyof ways [43,32,11]. Coarse steering of the beamscan be done using gimbals, and finer alignmentcan be done using Fast Steering Mirrors (FSMs),

electro-optic devices or acousto-optic devices [43].Since the alignment can be disturbed due to move-ment of transmitter/receiver, or building sway, thetransmitter can either use a beam with higher coneangle to counter building sway [44], or use activebeam tracking techniques like photodiode arraysor CCD arrays [43]. Since very accurate steeringhardware and active tracking techniques can beexpensive, we expect the use of larger beam anglesto counter the slight alignment mismatch and build-ing sways, while losing on the link capacity a little.

Each node has the capability to perform routing,which is multi-hop between source and destinationnodes1. We also assume that wireless links can beset up in any direction with all the nodes withintransmission range. Since the transmission distanceis related to the power level of the node, the powerlevel and thus the transmission range of each nodecan be different. The wireless links are uni-direc-tional2. If there is a pair of uni-directional linksbetween two nodes, the link capacities may differ.The number of transmitters and receivers at eachnode is limited (which we call an interface con-straint), thereby restricting the number of nodes towhich it can connect.

We model the traffic as a collection of individualflows with Poisson arrival times with rate ki, expo-nential holding times (with mean Ti) and constantbit rate traffic (Ri) for each flow. The mean of theaggregate traffic demand for each ingress–egresspair (i) can be computed as kiTiRi. We generatethe traffic profile (consisting of the aggregate trafficdemands between ordered pairs of sources and des-tinations) using these mean aggregate demands.

The problem we address is to form a subgraphG 0 = (V,E 0) and compute a routing on the sub-graph, such that the interface constraints are satis-fied for all nodes in set V (i.e., the degree of eachnode is bounded by the number of available inter-faces), and we maximize the throughput while rout-ing the traffic profile. We consider both single-pathrouting, i.e., each aggregate demand should be rou-ted on a single path; and splittable routing, i.e., eachdemand can be split among multiple paths. We then


use this information to achieve good throughputand low blocking rates when the network is func-tional. The offline part of the algorithm forms thissubgraph, which we call topology control andcomes up with routes and bandwidth reservationsfor the ingress–egress pairs given in the traffic pro-file. The topology computed is set up and the onlinepart of the algorithm uses the information com-puted in the offline phase to exercise admission con-trol and select routes for individual flows. Theserver should recompute the topology, routes andbandwidth reservations whenever either the trafficprofile or the (backbone) node locations change sig-nificantly. We do not anticipate that this would bedone more often than hourly. The nodes then usethis information to perform routing and traffic engi-neering on incoming flows. We show the problem tobe NP-Hard in Theorem 3.1 [27].

Theorem 3.1. Given a graph G = (V,E) and a traffic

profile consisting of traffic demands between different

vertices of G, the problem of finding a degree

constrained subgraph G 0 = (V, E 0) and routes for the

traffic demands such that the total demand routed is

maximized is NP-Hard.

Proof. Consider a small amount of traffic betweeneach pair of nodes in the network (small enoughnot to violate any link bandwidth constraints).The problem of maximizing the throughput reducesto finding a connected subgraph (satisfying thedegree constraints) here. We can remove the extraedges and the problem reduces to finding a degree-constrained spanning tree, which is a known NP-Hard problem. A special case is where we have adegree constraint of one incoming and one outgoingedge at each node. In this case, the problem reducesto finding a hamiltonian cycle, which is known to beNP-Complete [20]. h

Fig. 1. (a) Potential topology, (b) topology after routing t38, (c)topology after routing t38, t18, t45 and (d) topology after routingall demands.

4. Integrated topology control and single-path routing

framework

We propose a framework for finding the topol-ogy, single-path routes and bandwidth reservationsin an integrated way, so as to maximize the through-put while satisfying the interface and bandwidthconstraints. Given a potential topology and trafficprofile, we execute the following steps:

1. A demand is chosen based on some criteria and alocally optimal path (satisfying the interface and

bandwidth constraints) is computed for thedemand. If none exists, the demand is rejected.

2. If the path includes potential links, then thoselinks are marked as actual links.

3. The capacity of each link on the path in the exist-ing topology is updated (decreased) to incorpo-rate the bandwidth allocated to the demandrouted.

4. The topology is updated by eliminating thepotential links that lead to the violation of inter-face constraints, i.e., at the nodes for which thenumber of actual incoming (outgoing) linksequals the number of interfaces, the incoming(outgoing) potential links incident on (goingout of) those nodes are eliminated.

5. Steps 1, 2, 3 and 4 are repeated until all demandsare either provisioned or rejected. This way, atopology is created from the potential topologyand all the routes are computed for the demandsgiven in the traffic profile (the ones we are able toroute, the others are rejected).

As an example, assume that each node has twointerfaces available for establishing bidirectionallinks. The traffic profile is sorted in the order ofdecreasing demands, and demands are selected inthat order. The link capacity of each link is assumedto be 10 units. We use constrained shortest-pathrouting for path selection, with the constraints beingthe limited interfaces and bandwidth. The weight ofeach link is assumed to be 1. Let the traffic demandsbe: t38 = 6, t18 = 5, t45 = 3, t37 = 2. We compute theshortest path for the first demand t38 (3–5–8) usingthe potential topology as shown in Fig. 1a. Fig. 1bshows the topology after converting the potential

3 The route is non-unique, and we use a modified version ofDijkstra’s algorithm to find one of the possible shortest paths.


links along the path 3–5–8 to actual links and allo-cating the bandwidth for the demand. In Fig. 1b,the actual links are represented by thick lines andthe potential links are represented by thin lines. Asthere are no more interfaces available for node 5to establish a link with other nodes, the potentiallink between node 4 and 5 is eliminated, as can beseen by comparing Fig. 1a and b.

Fig. 1c shows the updated network, reflecting therouting of t18 and t45. Now we compute the shortestpath for the demand t37 using the modified network,as shown in Fig. 1c. There are two paths availablefor t37: (3–5–8–7 and 3–4–2–1–6–7). Since the avail-able bandwidth along the path 3–5–8–7 is 1, whichis less than the demand, t37 is routed on 3–4–2–1–6–7, and the network topology is updated to getthe final topology as shown in Fig. 1d.

5. Rollout algorithms for topology control and routing

We propose heuristics for demand ordering andpath selection for the integrated topology controland routing framework. We then use the rollouttechnique to improve the heuristics to obtain poten-tially near-optimal solutions.

5.1. Basic rollout algorithm

Rollout is a general method for obtaining animproved policy for a Markov decision processstarting with a base heuristic policy [7]. The rolloutpolicy is a one step look-ahead policy, with the opti-mal cost-to-go approximated by the cost-to-go ofthe base policy. We use the specialization of rolloutto discrete multistage deterministic optimizationproblems. Consider the problem of maximizingG(u) over a finite set of feasible solutions U. Sup-pose each solution u consists of N componentsu = (u1, ..,uN). We can think of the process of solv-ing this problem as a multistage decision problemin which we choose one component of the solutionat a time. Suppose that we have a heuristic algo-rithm, the so-called ‘‘base heuristic’’, that given apartial solution (u1, ..,un), (n < N), extends it to acomplete solution (u1, .., uN). Let H(u1, ..,un) =G(u1, ..,uN). In other words, the value of H on thepartial solution is the value of G on the full solutionresulting from application of the base heuristic. Therollout algorithm R takes a partial solution(u1, ..,un�1) and extends it by one component toR(u1, ..,un�1) = (u1, ..,un) where un is chosen tomaximize H(u1, ..,un). Thus, the rollout algorithm

considers all admissible choices for the next compo-nent of the solution and chooses the one that leadsto the largest value of the objective function if theremaining components are selected according tothe base heuristic.

It can be shown that under reasonable condi-tions, the rollout algorithm will produce a solutionwhose value is at least as great as the solution pro-duced by the base heuristic. We proved in [26] thatthe rollout algorithms proposed here perform betterthan the heuristic. Note that the heuristic may be agreedy algorithm, but the rollout algorithms are notgreedy as they make a decision based on the finalexpected value of the objective function, and noton the increment to the value of the objective func-tion at that decision step.

5.2. Rollout algorithms for topology control and

routing

We propose three different rollout algorithms:index rollout, route rollout and integrated rollout.We start by explaining the base heuristic.

5.2.1. Base heuristic

The base heuristic works as follows: Suppose thata partial topology has been obtained by choosingroutes for the first n demands (t1, .., tn) from the traf-fic profile. The base heuristic routes the remainingdemands in decreasing order of magnitude. Foreach demand, it chooses a route using constrainedshortest path first (CSPF)3, with constraints beingthat of available interfaces and bandwidth. Thus,tn+1 is the largest remaining demand. The route cho-sen for this demand is a shortest unidirectional pathin the partial topology satisfying the constraints.This means that every actual link in the path musthave sufficient residual bandwidth for the demand;every potential link in the path must have an avail-able transmitter at its head node and an availablereceiver at its tail node. If there is no feasible path,then the demand is blocked. If there is a feasiblepath, the heuristic updates the topology by deletingthe potential links that violate the interface con-straints and decreasing the available bandwidth ofthe links on that path (see Section 3 for descriptionof this framework). Once tn+1 has been routed, thebase heuristic routes the next largest demand tn+2


in the same way using the partial topology existingafter tn+1 has been routed. The base heuristic algo-rithm continues in this way until all demands havebeen routed (or assigned null routes). The base heu-ristic is derived from the single hop traffic maximi-zation heuristics for topology control and routingin wireline optical networks, [6,39,33,45]. The maindifference is that links are multi-hop in wireless net-works, due to which interfaces are consumed at allintermediate nodes, while we need to take care ofinterfaces only at end-points of lightpaths in wire-line networks. Another difference is that the routingand wavelength assignment (RWA) is discrete inwireline networks, while we check for bandwidthconstraints on each link, which is continuous.

5.2.2. Index rollout algorithm

Index rollout seeks to optimize the order in whichthe traffic demands are routed. The index rolloutalgorithm works as follows: In the first step, the roll-out algorithm uses CSPF to route the demand t1

determined by the requirement that it maximizethe total network throughput when the base heuris-tic is used to complete the topology starting with t1.

Now, suppose that the demands (t1, .., tn�1) havebeen routed in this order by the rollout algorithm.In the next step, the rollout algorithm uses CSPFto route the demand tn determined by the require-ment that it maximize the total network throughputwhen the base heuristic is used to complete thetopology starting with (t1, .., tn). In other words,routing tn next minimizes the sum of the remainingdemands that are blocked. After routing eachdemand, the index rollout updates the topology toeliminate the links that violate the interface con-straints, and decreases the residual bandwidth ofthe links on the path on which this demand isrouted.

5.2.3. Route rollout algorithm

Route rollout seeks to optimize the selection ofpath4 for each demand when the demands are con-sidered in a fixed order. We consider the demands indecreasing order of magnitude. Let (t1, .., tN) be theordered sequence of demands. The base heuristicworks as follows: Suppose that a partial topologyhas been obtained by choosing routes (p1, ..,pn) forthe first n demands (t1, .., tn). The base heuristicroutes the remaining demands (tn+1, .., tN) sequen-

4 The algorithm evaluates multiple constrained shortest paths.

tially using CSPF. The route rollout algorithmworks as follows: Fix an integer K > 1. In the firststep, the rollout algorithm considers at most K fea-sible shortest paths as candidates for the route p1 forthe demand t1. For each potential choice of p1 ituses the base heuristic to complete the topologyby routing the remaining traffic demands. The roll-out algorithm then selects for p1 the candidate thatresults in the maximum total network throughput.Now, suppose that the demands (t1, .., tn�1) havebeen given routes (p1, ..,pn�1) by the rollout algo-rithm. In the next step, the rollout algorithm consid-ers at most K feasible shortest paths as candidatesfor the route pn for the demand tn. For each poten-tial choice of pn it uses the base heuristic to completethe topology by routing the remaining trafficdemands. The rollout algorithm then selects for pn

the candidate that results in the maximum total net-work throughput. Note that if there is only one fea-sible shortest path for a traffic demand, the routingdecision made by the rollout algorithm coincideswith the decision made by the base heuristic.

It might appear desirable to consider all feasibleshortest paths as candidates for pn. However, anexponential number of shortest paths may exist.Consequently, we limit the number of paths consid-ered to K, where the upper bound K is chosen smallenough to allow reasonable computation time giventhe size of the network.

5.2.4. Integrated rollout algorithm

In integrated rollout, we make the decisions ofchoosing the demand to be routed and the path tobe used for that demand simultaneously. In inte-grated rollout, each component of a solution is a pair(tk,pk) consisting of a traffic demand and its path.Thus, the algorithm seeks to optimize the sequence((t1,p1), .., (tN,pN)). The base heuristic takes a partialsolution ((t1,p1), .., (tn,pn)) and extends it to a com-plete solution by choosing the remaining trafficdemands (tn+1, .., tN) in order of decreasing magnitudeand choosing paths (pn+1, ..,pN) (some of which maybe null) for these traffic demands sequentially usingCSPF. The integrated rollout algorithm works as fol-lows: In the first step it considers all pairs (t1,p1) wheret1 is any of the traffic demands and p1 is any one of amaximum of K feasible shortest paths for t1. It selectsthe pair (t1,p1) that gives the maximum total networkthroughput when the base heuristic is used to extend itto a full topology. Now, if the rollout algorithm hasproduced the sequence ((t1,p1), .., (tn�1,pn�1)), it con-siders pairs (tn,pn) where tn is a remaining demand

Table 2Average bandwidth guarantees

Heuristic Route rollout Index rollout Integrated rollout

0.8782 0.9326 0.9582 0.9597


and pn is any one of a maximum of K feasible shortestpaths for tn. It selects the pair (tn,pn) that maximizesthe total network throughput when the base heuristicis used to extend ((t1,p1), .., (tn,pn)) to a full solution.

Table 3Average throughput


0.7729 0.8232 0.8520 0.8542

5.3. Online routing and admission control

After the topology and routing is determined, thetopology is set-up, and the bandwidth reservationinformation and the route for each ingress–egresspair is given to the ingress node for that pair. When-ever a call (new request of traffic between an ingress–egress pair) arrives, the ingress router checks to see ifthere is enough bandwidth left from the bandwidthreserved for this pair. If there is bandwidth left, thenthe flow is routed through the path stored from theoffline phase. We may have additional unreservedbandwidth on some links in the network (the band-width left unreserved), so in the case of reservedbandwidth being exhausted for an ingress–egresspair, the unreserved bandwidth is used (on a first-come-first-served basis). If the call cannot be routedusing the reserved bandwidth or the extra unreservedbandwidth, it is blocked.

5.4. Simulation results and analysis

The network we considered for simulations wasassumed to have the parameters listed in Table 1.All the nodes were assumed to have the same trans-mission range.

The simulation was run 10 times, and in each sim-ulation the network topology was formed startingwith these parameters. Table 2 shows the average

Table 1Simulation parameters

Number of nodes in the network(uniformly distributed)

50

Average degree of each node 7.5Number of receive interfaces at a node 3Number of transmit interfaces at a node 3Link capacity (unidirectional) 100Number of nodes capable of being a

source/destination12

Number of source–destination pairs 100Poisson rate (ki), uniformly distributed 10–20Mean of holding time (Ti), uniformly

distributed1–2

Bit rate of individual calls 1Number of shortest paths considered in

rollout algorithms (K)4

Weight of each link in shortest pathcomputation

1

fractional throughput (bandwidth guarantees/totaldemand) for the heuristic and the rollout algorithms.

Table 2 shows that compared to the heuristic, theroute rollout performs nearly 6.2% better, the indexrollout performs 9.1% better and the integrated roll-out performs 9.3% better. So, generally the inte-grated rollout is expected to perform the bestamong these rollouts. Another observation fromthe results is that the index selection is more criticalthan the selection of routes from among multipleroutes. This can be inferred from the fact that theindex rollout works much better than the route roll-out while the integrated rollout does not work thatmuch better than the index rollout.

The algorithms have been shown to have similarperformance under various traffic conditions (light,medium, heavy) in [28].

The network was setup and Poisson traffic withexponential holding times and constant bit rate(the parameters being the same as provided to off-line phase) was generated, and the network wasrun for 30 units of time for each of the 10 simula-tions. In each simulation, the traffic for evaluatingthe heuristic was the same as that for the rollout.Table 3 gives the average throughput (which is thesame as call acceptance rate as traffic is CBR withsame rate for all pairs) for each of the algorithms.As the results show, the relative performance is sim-ilar to the bandwidth guarantees we could achieve inthe offline phase. The throughput is lower thanguaranteed since the guarantees were for a constantarrival rate (equal to the mean arrival rate of thePoisson process in the simulation), while it actuallyis Poisson with the given mean arrival rate, so thereare time periods when the arrival rate is higher,leading to lower throughput.

6. Topology control and multi-path routing

In this section, we propose algorithms for topol-ogy control and multi-path routing. We first describe


the multi-commodity flow formulation of the multi-path routing problem on a fixed topology, which is alinear program and can be solved efficiently. We thenpropose algorithms based on maximum weightmatching [36] for topology computation.

6.1. Multi-commodity flow formulation of routing

We set up the problem of routing a given trafficprofile over a computed topology for maximizingthe throughput as a linear multi-commodity flowproblem [42]. Let there be M commodities (profileentries, the value of each entry is bi), N nodes andL links in the network. We add a dummy link (veryhigh cost, very large capacity) between the sourceand destination of each commodity to achieve feasi-bility (thus, there are M such links). Let xl

i be theamount of commodity i routed through link l. Letcl represent the cost of each link, which is 1 for anactual link for our objective of maximizing thethroughput. Let the set of incoming and outgoinglinks at node j be denoted by Ij and Oj respectively.Let si and di represent the source and destination ofprofile entry i. Let rl represent the capacity of link l.Eq. (1a) achieves the objective of maximizing thethroughput as the algorithm tries to route on theactual links due to large cost of the dummy links.Eq. (1b) represents the bandwidth constraints.Eqs. (1c) and (1d) represent the flow conservationlaws.

minXLþM

l¼1

cl

XM

i¼1

xli

!ð1aÞ

s:t:XM

i¼1

xli 6 rl; 8l 2 f1; ::; Lg; ð1bÞ

Xl2Ij

xli ¼

Xl2Oj

xli ; 8j 2 f1; ::; Ng � fsi; dig;

8i 2 f1; ::; Mg; ð1cÞXl2Oj

xli �Xl2Ij

xli ¼ bi; j ¼ si; 8i 2 f1; ::; Mg;

ð1dÞxl

i P 0; 8i 2 f1; ::; Mg; 8l 2 f1; ::; LþMg:ð1eÞ

6.2. Topology control using matching theory

We present an algorithm based on maximumweight matching. The algorithm is outlined belowand explained in the following subsections.

1. Weight the links in the initial graph to favor thelinks that are expected to carry higher traffic.

2. Construct an auxiliary graph based on the net-work. We will explain the construction procedurelater.

3. Find a maximum weight matching [36] to com-pute a maximum weight subgraph that satisfiesthe interface constraints.

4. Construct a topology based on the matchingoutput.

5. Find the routing by solving the linear program ofSection 6.1 on this topology.

6. Modify the topology sequentially and solve theMCF linear program again each time, andfinally, keep the topology that gives the maxi-mum throughput.

6.2.1. Initial weight assignment

We propose three strategies for weighting thenetwork links for construction of the auxiliarygraph. The way we map the problem to maximumweight matching problem, if we give the sameweight to all links in the network, the output topol-ogy will have the maximum number of links whilesatisfying the degree constraints (as we try to maxi-mize the weight during maximum weight matching,same weight to all edges would result in maximizingthe number of edges). We call the algorithm usingthis policy Uniform Weighted Matching (UWM).As our objective is maximizing the throughput, soit may be better to give extra weight to edges thatare expected to carry more traffic. We call the algo-rithm using this policy as Traffic Weighted Match-ing (TWM), and explain it below:

1. Give a weight of one to all edges.2. Find (maximum) K shortest paths of same length

for each traffic profile (over the potentialtopology).

3. Each time a link occurs in a path, increment itsweight by profile(i)/numSP, where profile(i) isthe value of the profile entry, and numSP thenumber of shortest paths found (6K) for thatentry.

Another possibility is to assign weights accordingto the number of paths a link occurs on, irrespectiveof the amount of traffic. In this case, we incrementthe weight of a link by one in step 3 above. We callthe algorithm using this strategy Flow WeightedMatching (FWM). We work with shortest paths as


the multi-commodity flow formulation will prefershorter paths for a commodity because it minimizesthe cost function of Eq. (1a) (to maximize thethroughput).

6.2.2. Construction of auxiliary graph

We now explain the procedure for constructingthe auxiliary graph to be used as an input for maxi-mum weight matching. Given a graph G = (V,E)(that corresponds to the potential network) withedge weights as explained in Section 6.2.1, we forma graph G 0 = (V 0,E 0) and give it as an input to themaximum weight matching problem. Let the num-ber of transmit and receive interfaces (i.e., incomingand outgoing degree constraints) at each vertex beD. Fig. 2 shows an example potential topology withD = 2. The steps of mapping are explained below.

1. For each vertex, form 2D vertices in graph G 0. Dof them correspond to the transmit interfaces,and D to receive interfaces.

2. For each edge e in G, form two vertices (te, he) inG 0, and add an edge of weight zero between them.

3. For each edge e in G with weight we, add edges ofweight we between te (in G 0) and all transmitinterface vertices of the tail vertex of e. Also,add edges of weight we between he and all receiveinterface vertices of the head vertex of e. Fig. 3shows G 0 for our example. T, R and E refer to

A B

C

D

E

Fig. 2. Potential topology, D = 2.

T

R R

T

E

E

EE

EE

E

E

R

R

R T

T

T

0

0

0

0

Fig. 3. Modified graph from potential topology.

the vertices corresponding to transmit interfaces,receive interfaces and edges in G respectively. Theedges shown without weights have a weight of 1.

4. Add a clique with 2DN vertices to the graph G 0,with each edge having a weight zero. Add zeroweight edges between each of these vertices andeach of the vertices in G 0 that correspond to thetransmit and receive interfaces of the vertices ingraph G.

5. Sum the weights of all the edges in G 0 and addthat to the weight of all edges in G 0. We do thisto ensure we get a perfect matching using a max-imum weight matching algorithm.

We solve the maximum weight matching problemon G 0, and deduce the resulting topology based onthe result we get. We show the rules for mappingfrom the output of matching to the graph represent-ing the topology: Fig. 4a shows the scenario (a sub-graph from the output of matching algorithm) whentwo vertices will have an edge between them in thefinal topology. Fig. 4b shows the case when two ver-tices that had an edge between them in G will nothave the edge in the resulting topology (as theyare not connected to the edge vertices correspondingto the edge between them). We detect such sub-graphs in the output graph from matching algo-rithm (the output graph will be composed of suchsubgraphs only), and use these rules to deduce theresulting topology.

We added a clique to the graph G 0 to avoid thescenario in which we cannot deduce the topologyfrom the result of the matching algorithm. Fig. 4cshows the case when this has happened betweentwo vertices. In this case, one of the vertices ismatched to the edge vertex in G 0, while the othervertex is not matched with the corresponding edgevertex. This can be avoided by having perfectmatching, and for achieving that we add a clique

T E E R

T E E R

T E E R

a

b

c

Fig. 4. Rules for deducing connectivity: (a) connected vertices,(b) vertices not connected and (c) connection between verticesundecidable.

T

R R

T

E

E

EE

EE

E

E

R

R

R T

T

T

Fig. 5. Matching algorithm output.

A B

C

D

E

Fig. 6. Final topology.

Table 4Simulation parameters

Number of nodes in the network(uniformly distributed)

20

Average degree of each node(no. of potential neighbors)

6.5

Number of receive interfaces at a node 3Number of transmit interfaces at a node 3Link capacity (unidirectional) 100Number of nodes capable of being a

source/destination20

Number of source-destination pairs 160Aggregate traffic between each pair,

uniformly distributed1–40

Number of shortest paths considered inrollout algorithms

4

Threshold (x) for sequential topologychange

20

Number of shortest paths considered forweighting in matching

3


of size 2DN and connect each of them to all the ver-tices in G 0 that correspond to transmit and receiveinterfaces of vertices in G. We accommodate theworst case in which all the vertices will be discon-nected in the final topology.

Fig. 5 shows the output (minus the clique verticesand corresponding edges) of the matching algorithmand Fig. 6 shows the final topology we get for theexample network of Fig. 2.

6.2.3. Topology change strategy

We solve the multi-commodity flow problem (asexplained in Section 6.1) on the topology we getfrom the algorithm explained in Section 6.2. Wesequentially change this topology and solve themulti-commodity flow problem on the resultingtopologies to get an improvement in the through-put. The algorithm for changing the topology is asexplained below:

• Make a list of the profile entries for which wecould route less than x% of the demand indecreasing order of demand.

• For the first entry in this list, find (maximum) Kshortest paths each in the potential topology andthe current topology. Form the first path that ispresent in the potential topology, but not in thecurrent topology by deleting the least loadedlinks (using routing given by the MCF) at eachof the interface-starved nodes in the current

topology on this path. If all the paths are thesame then repeat this step for the next entry inthe list.

• Solve the multi-commodity flow problem for thischanged topology. If the throughput is more thanthe throughput in the current topology thenchange the current topology to this topologyand update the list by deleting the entries forwhich we have routed more than x% on thistopology. If the throughput is less than before,then let the current topology remain the sameand start with step 2 for the next entry in the list.

We finally keep the topology we have at the endof this procedure.

6.3. Simulation results and discussion

We simulate two types of networks. In the firstset of simulations, all nodes in the network can beingress or egress nodes. In the second set, only asmall subset of nodes in the network are ingress oregress nodes.

6.3.1. Simulation set 1

The network used for simulations was assumedto have the parameters listed in Table 4.

The simulation was run on a different randomnetwork and random profile 10 times and in eachsimulation, the network topology was formed start-ing with these parameters. The matching algorithmused is an implementation of Gabow’s N-cubedweighted matching algorithm [18].

Table 5Average bandwidth guarantees for extended rollout algorithms


0.7090 0.7223 0.7335 0.7550

Table 6Average bandwidth guarantees for matching based algorithms

UWM FWM TWM UWM1 FWM1 TWM1

0.7178 0.7606 0.7720 0.6650 0.7294 0.7535

Table 7Average bandwidth guarantees for matching based algorithms

UWM FWM TWM UWM1 FWM1 TWM1

0.9045 0.8749 0.8797 0.8436 0.8698 0.8742


For comparison, we implemented rollout algo-rithms followed by the MCF formulation of Section6.1 (that we call extended rollout algorithms), inwhich the rollout algorithms are executed, and thetopology is taken to be the output of those algo-rithms. The MCF is solved on that topology toget a multi-path routing. Table 5 shows the averagebandwidth guarantees for the extended rolloutalgorithms. Table 6 shows the average bandwidthbuarantees for the matching based algorithms. Aswe can see, the algorithm with Traffic WeightedMatching (TWM) works the best, followed by FlowWeighted Matching (FWM), Uniform WeightedMatching (UWM). Traffic Weighted Matchingworks 8.88% better than the heuristic for rolloutand 2.25% better than the integrated rollout. Thus,TWM and FWM work better than the extendedrollout algorithms, and the execution time is muchless than the rollout algorithms (discussed in nextsection). Also, rollout-based algorithms work betterthan UWM.

Table 6 also shows the average bandwidth guar-antees we get in the proposed algorithms withoutusing the sequential topology change strategy (wecall the corresponding algorithms UWM1, FWM1,TWM1). The results with and without sequentialchange show that the improvement in bandwidthguarantees is the maximum in UMW1 followed byFWM1 and TWM1. This, along with the results ofTable 6, shows that TWM works the best amongthese three strategies, and weighting strategiesof TWM and FWM are good for this networkmodel.

Table 8Average bandwidth guarantees for extended rollout algorithms


0.8935 0.9222 0.9247 0.9400

6.3.2. Simulation set 2

In this set of simulations, the networks have 50nodes and the number of nodes capable of beingsource/destination is 12. The number of source-des-tination pairs is fixed at 90. The nodes have an aver-

age degree of 7.5. All other parameters are the sameas in simulation set 1.

The simulation was run on a different randomnetwork and random profile 10 times, and in eachsimulation the network topology was formed start-ing with these parameters.

Table 7 shows the average bandwidth guaranteesfor the matching based algorithms. The algorithmwith UWM works the best, followed by TWM

and FWM. Table 8 shows the average bandwidthguarantees for the extended rollout algorithms.Results show that the extended rollout algorithmswork better than the matching-based algorithms.Thus, in networks with small number of source/des-tination nodes, the weighting strategies of TWMand FWM are not suitable, and rollout-based algo-rithms work better than the proposed matching-based algorithms. The reason seems to be that therollout algorithms are sequential, and treat eachsource–destination pair separately, while the match-ing-based algorithms compute a maximum totalweight topology, with weights heuristically depen-dent on the traffic and expected routes. In case ofrelatively small number of source–destination pairs,the proposed weighting strategies as well as the ideaof looking at total weight according to these strate-gies do not seem to work as well as treating thoseseparately (as in rollout algorithms).

Table 7 also shows the average bandwidth guar-antees we get in the proposed algorithms withoutusing the sequential topology change strategy. Theresults with and without sequential change showthat the improvement in bandwidth guarantees isthe maximum in UWM, followed by FWM andTWM.

The problem of finding a degree constrained con-nected topology is NP-Hard [20]. In the topologiescomputed by our algorithms, traffic could berouted between all ingress–egress pairs in almostall cases.

Table 9Computational time complexity

Route rollout O(M2N2)Index rollout O(M3N2)Integrated rollout O(M3N2)Matching algorithms O(N4logN)


7. Computational complexity

7.1. Topology control and single-path routing

algorithms

We first discuss the worst case time complexity ofsingle-path routing algorithms. Let the number ofnodes in the network be N, number of (potential)edges be E (=O(N2)) and the number of aggregatedemands in the traffic matrix be M. We use a mod-ified version of Dijkstra’s shortest path algorithm[14] as a heuristic for finding the shortest paths. Itis modified to take care of the interface and band-width constraints while finding a shortest path. Asthe topology at any intermediate state of the algo-rithms is not expected to be sparse, so the processof finding a shortest path takes O(N2) time. We sortthe profile by decreasing order of traffic demands,which takes O(M logM) time. The time complexityof the heuristic algorithm is O(MN2), as shortestpaths are computed M number of times. If the setof source/destination nodes is constant, then so isthe number of aggregate demands. In this case,the complexity becomes O(N2).

The time complexity of the route rollout algo-rithm is O(M2N2), as K is fixed. This complexity isdue to the fact that at each decision step, O(M)shortest paths are computed, and there are M deci-sion steps in the algorithm. In the case of fixed M,the complexity is O(N2). The time complexity forthe index rollout algorithm is O(M3N2). At eachdecision step in the algorithm, O(M2) shortest pathsare computed, and there are M decision steps in thealgorithm resulting in the above complexity. Thisalso reduces to O(N2) for fixed M. The complexityfor the integrated rollout is the same as index rollouttime is scaled by K, which is a constant.

In the case where each node in the network can be asource or a destination, M scales as N2 and the com-plexity of the heuristic algorithm becomes O(N4),while the route rollout algorithm takes O(N6),and the other two rollout algorithms take O(N8)time.

7.2. Complexity of matching-based algorithms

The computational complexity of the algorithmscan be broken into the following steps:

1. Weighting: It calculates shortest paths (takesO(N2) time for each path calculation) for O(M)flows. So, this takes O(MN2) time.

2. Maximum Weight Matching: There are N verti-ces, O(N2) edges in the original graph G. In thegraph G 0 (input to matching), we createO(N + N2) vertices from the vertices and edgesof graph G, and add O(N) vertices that form a cli-que. So, number of vertices in G 0 is N 0 = O(N2).In G 0, there are O(N2) edges between the verticescorresponding to edges and vertices in G. Thereare O(N2) edges in the clique that we add. Thereare edges between all vertices of the clique (O(N)vertices) and all O(N) vertices that correspond tovertices in G. So, number of edges in G 0,E 0 = O(N2). Maximum weight matching takesO(E 0N 0logN 0) time and thus matching takesO(N4logN) time.

The maximum order of M is O(N2), and so themaximum weight matching step determines theorder of the proposed algorithms (not countingthe time taken to solve the MCF). Thus, these partsof the algorithms take O(N4logN) time, with N

being the number of nodes in the network. Thiscomplexity is much lower than that for route rollout(O(N6)) and index and integrated rollout algorithms(O(N8)). The heuristic used by these rollout algo-rithms takes O(N4) time.

The worst case time complexity of the multi-pathalgorithms is dominated by the worst case complex-ity of solving the linear program (LP), which takesO((MN + E)3.5) time using interior point methods[8]. This worst case bound is misleading as currentLP-solvers like CPLEX [10] are very fast for mostinstances of moderately sized linear programs, andthus the multi-path algorithms are much faster thanthe single-path rollout algorithms in our simula-tions. To summarize, we tabulate the computationalcomplexity of the proposed algorithms in Table 9.

8. Conclusion

We consider the problem of integrated topologycontrol and routing in Free Space Optical (FSO)wireless mesh networks. FSO links have characteris-tics that make them more suitable than RF links for


use in mesh networks, where certain bandwidthguarantees need to be provided to end-users. Asthe number of FSO transceivers at each node isscarce, we consider the critical problem of topologycontrol so that the network throughput is high for agiven traffic estimate. We prove the problem NP-Hard and propose efficient algorithms for topologycontrol and routing (both single-path and multi-path). The simulation results show significant gainsover simple algorithms.

References

[1] IEEE 802.15 standard group, <http://www.ieee802.org/15/>.[2] IEEE 802.16 standard group, <http://www.ieee802.org/16/>.[3] J. Akella, C. Liu, D. Partyka, M. Yuksel, S. Kalyanaraman,

P. Dutta, Building blocks for mobile free-space-opticalnetworks, in: IFIP/IEEE International Conference on Wire-less and Optical Communications Networks (WOCN), 2005.

[4] J. Akella, M. Yuksel, S. Kalyanaraman, Error analysis ofmulti-hop free-space-optical communication, IEEE Interna-tional Conference on Communications (ICC) 3 (2005) 1777–1781.

[5] I.F. Akyildiz, X. Wang, W. Wang, Wireless mesh networks:a survey, Computer Networks 47 (4) (2005) 445–487.

[6] D. Banerjee, B. Mukherjee, Wavelength-routed opticalnetworks: Linear formulation, resource budgeting tradeoffs,and a reconfiguration study, IEEE/ACM Transactions onNetworking 8 (5) (2000) 598–607.

[7] D.P. Bertsekas, Dynamic Programming and Optimal Con-trol, vol. 1, Athena Scientific, 2000.

[8] S. Boyd, L. Vandenberghe, Convex Optimization, Cam-bridge University Press, 2003.

[9] J. Cao, D. Davis, S.V. Wiel, B. Yu, Time-varying networktomography: Router link data, American Statistical Associ-ation Journal 95 (2000) 1063–1075.

[10] CPLEX, <http://www.cplex.com>.[11] J. Derenick, C. Thorne, J. Spletzer, Control system analysis

for ground/air-to-air laser communications using simulation,IEEE/RSJ International Conference on Intelligent Robotsand Systems (IROS) (2005) 3990–3996.

[12] A. Desai, J. Llorca, S. Milner, Autonomous reconfigurationof backbones in free space optical networks, IEEE MIL-COM (2004) 1226–1232.

[13] A. Desai, S. Milner, Autonomous reconfiguration in free-space optical sensor networks, IEEE JSAC Optical Com-munications and Networking Series 23 (8) (2005) 1556–1563.

[14] E.W. Dijkstra, A note on two problems in connection withgraphs, Numerische Mathematik 1 (1959) 269–271.

[15] N.G. Duffield, M. Glossglauser, Trajectory sampling fordirect traffic observation, IEEE/ACM Transactions onNetworking 9 (3) (2001) 280–292.

[16] A. Feldmann, A. Greenberg, C. Lund, N. Reingold, J.Rexford, F. True, Deriving traffic demands for operationalIP networks: Methodology and experience, IEEE/ACMTransactions on Networking 9 (3) (2001) 265–279.

[17] A. Feldmann, J. Rexford, R. Caceres, Efficient policies forcarrying web traffic over flow-switched networks, IEEE/ACM Transactions on Networking 6 (6) (1998) 673–685.

[18] H.N. Gabow, Implementation of algorithms for maximummatching on nonbipartite graphs, Ph.D. thesis, StanfordUniversity, 1973.

[19] V. Gambiroza, B. Sadeghi, E.W. Knightly, End-to-endperformance and fairness in multihop wireless backhaulnetworks, ACM Mobicom (2004) 287–291.

[20] M. Garey, D. Johnson, Computers and Intractability: AGuide to the theory of NP-Completeness, Freeman andCompany, 1979.

[21] P.C. Gurumohan, J. Hui, Topology design for free spaceoptical networks, ICCCN, 2003.

[22] J. Hauser, Draft PAR for IEEE 802.11 ESS mesh, IEEEDocument Number IEEE 802.11-03/759r2.

[23] T.-H. Ho, S.D. Milner, C.C. Davis, Fully optical real-timepointing, acquisition, and tracking system for free spaceoptical link, in: G. Stephen Mecherle (Ed.), SPIE, Free-Space Laser Communication Technologies XVII, vol. 5712.2005, pp. 81–92.

[24] H. Izadpanah, T. Elbatt, V. Kukshya, F. Dolezal, B.K. Ryu,High-availability free space optical and RF hybrid wirelessnetworks, IEEE Wireless Networks 10 (2) (2003) 45–53.

[25] M. Kalantari, A. Kashyap, K. Lee, M. Shayman, Networktopology control and routing under interface constraints bylink evaluation, in: Conference on Information Sciences andSystems, 2005.

[26] A. Kashyap, M. Kalantari, K. Lee, M. Shayman, Rolloutalgorithms for topology control and routing of unsplittableflows in wireless optical backbone networks, in: Conferenceon Information Sciences and Systems, 2005.

[27] A. Kashyap, S. Khuller, M. Shayman, Topology control androuting over wireless optical backbone networks, in: Con-ference on Information Sciences and Systems, 2004.

[28] A. Kashyap, Profile based topology control and routing inwireless optical networks, MS Thesis, University of Mary-land, 2004.

[29] A. Kashyap, A. Rawat, M. Shayman, Integrated backuptopology control and routing of obscured traffic in hybridRF/FSO networks, in: IEEE Globecom, 2006.

[30] A. Kashyap, M. Shayman, Routing and traffic engineering inhybrid RF/FSO networks, in: IEEE International Confer-ence on Communications (ICC), 2005.

[31] S. Khuller, K. Lee, M. Shayman, On degree constrainedshortest paths, in: European Symposium on Algorithms(ESA), 2005.

[32] T.I. King, H.H. Refai, J.J.S. Jr., Y. Lee, P.G. LoPresti,Control system analysis for ground/air-to-air laser commu-nications using simulation, in: IEEE Digital AvionicsSystems Conference (DASC), 2005.

[33] J.F. Labourdette, A. Acampora, Logically rearrageablemulti-hop lightwave networks, IEEE Transactions on Com-munications 39 (8) (1991) 1223–1230.

[34] E. Leonardi, M. Mellia, M.A. Marsan, Algorithms for thelogical topology design in WDM all-optical networks,Optical Networks Magazine, Premiere Issue 1 (1) (2000)35–46.

[35] J. Llorca, A. Desai, S. Milner, Obscuration minimization indynamic free space optical networks through topologycontrol, IEEE MILCOM (2004) 1247–1253.

[36] L. Lovasz, M.D. Plummer, Matching Theory, North-Hol-land, 1986.

[37] A. Medina, N. Taft, K. Salamatian, S. Bhattacharyya, C.Diott, Traffic matrix estimation: Existing techniques and new

http://www.ieee802.org/15/

http://www.ieee802.org/16/

http://www.cplex.com


directions, ACM SIGCOMM Computer CommunicationReview (2002) 161–174.

[38] U.N. Okorafor, D. Kundur, Efficient routing protocols for afree space optical sensor network, IEEE International Con-ference on Mobile Adhoc and Sensor Systems (2005) 251–258.

[39] R.M. Ramaswami, K.N. Sivarajan, Design of topologies: Alinear formulation for wavelength routed optical networkswith no wavelength changers, IEEE/ACM Transactions onNetworking 9 (2) (2001) 186–198.

[40] N.A. Riza, Reconfigurable optical wireless, IEEE LEOS 1(1999) 70–71.

[41] C. Singh, J. John, Y.N. Singh, K.K. Tripathi, Design aspectsof high performance indoor optical wireless transceivers, in:IEEE International Conference on Personal Wireless Com-munications (ICPWC), 2005.

[42] S. Suri, M. Waldvogel, D. Bauer, P.R. Warkhede, Profile-based routing and traffic engineering, Computer Communi-cations 24 (4) (2003) 351–365.

[43] P. Yan, J.J.S. Jr., H.H. Refai, P.G. LoPresti, An initial studyof mobile ad hoc networks with free space optical capabilities,in: IEEE Digital Avionics Systems Conference (DASC), 2005.

[44] M.O. Zaatari, Wireless optical communications systems inenterprise networks, The Telecommunications Review (2003)49–57.

[45] Z. Zhang, A. Acampora, Heuristic wavelength assignmentalgorithm for multihop wdm networks with wavelengthrouting and wavelength re-use, IEEE/ACM Transactions onNetworking 3 (3) (1995) 281–288.

[46] J. Zhuang, M.J. Casey, S.D. Milner, S.A. Gabriel, G.Baecher, Multi-objective optimization techniques in topol-ogy control of free space optical networks, IEEE MILCOM(2004) 430–435.

Abhishek Kashyap received B.Tech. inElectrical Engineering from the IndianInstitute of Technology, Delhi in 2001;and M.S. and Ph.D. in Electrical Engi-neering from University of Maryland,College Park in 2004 and 2006 respec-tively.

His research interests include wirelessand wireline networks, graph algo-rithms, and discrete optimization. Hehas received two patents for his work

with IBM India Research Laboratory.

Mehdi Kalantari is an assistant researchscientist at the Electrical and ComputerEngineering department of the Univer-sity of Maryland (UMD). He receivedhis B.Sc. and M.Sc. degrees in ElectricalEngineering from the Sharif Universityof Technology, Tehran, Iran 1996, and1998, respectively. After gaining severalyears of industry experience in controland communication systems during1996–2000, he started his Ph.D. studies

at UMD in 2000, where he received Ph.D. in Electrical and

Computer Engineering in 2005, and since then he has workedthere as an assistant research scientist. His research interestsinclude Communication Theory, Distributed Denial of Service(DDoS) defense, and modeling and analysis of Wireless Net-works. He received Dean’s Honor Award of the Sharif Universityof Technology in 1996, Business Plan Competition Award ofUMD in 2004, and Award for Entrepreneurship of UMD in2006.

Samir Khuller received his M.S. andPh.D. from Cornell University in 1989and 1990, respectively. He spent 2 yearsas a Research Associate at the Institutefor Advanced Computer Studies at theUniversity of Maryland, before joiningthe Computer Science Department in1992, where he is a Professor and Asso-ciate Chair in the Department of Com-puter Science.

His research interests are in graphalgorithms, discrete optimization, and computational geometry.He has published about 130 journal and conference papers, and
several book chapters on these topics. He received the NationalScience Foundation’s Career Development Award, the Dean’sTeaching Excellence Award and also a CTE-Lilly Teaching Fel-lowship. In 2003, he and his students were awarded the ‘‘Bestnewcomer paper’’ award for the ACM PODS Conference. Hereceived the University of Maryland’s Distinguished ScholarTeacher Award in 2007.
Mark A. Shayman received the Ph.D.degree in applied mathematics fromHarvard University, Cambridge, MA, in1981.

He served on the Faculty of Wash-ington University, St. Louis, MO, andthe University of Maryland, CollegePark, where he is currently Professor ofElectrical and Computer Engineeringand Associate Dean for Faculty Affairsin the A. James Clark School of Engi-

neering. His research interests are in communication networks,including optical, wireless and sensor networks.

He received the Donald P. Eckman Award from the AmericanAutomatic Control Council and the Presidential Young Investi-gator Award from the National Science Foundation. He hasserved as Associate Editor of the IEEE Transactions on Auto-matic Control.

Documents

Integrated topology control and routing in wireless optical mesh networks