Front. Comput. Sci., 2013, 7(3): 446–457

DOI 10.1007/s11704-013-2108-4

Topology-aware virtual network embedding based oncloseness centrality

Zihou WANG 1, Yanni HAN1, Tao LIN1, Yuemei XU1, Song CI1,2, Hui TANG1

1 High Performance Network Laboratory, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China

2 Department of Computer and Electronics Engineering, University of Nebraska-Lincoln, NE 68182, USA

c© Higher Education Press and Springer-Verlag Berlin Heidelberg 2013

Abstract Network virtualization aims to provide a way to

overcome ossification of the Internet. However, making effi-

cient use of substrate resources requires effective techniques

for embedding virtual networks: mapping virtual nodes and

virtual edges onto substrate networks. Previous research has

presented several heuristic algorithms, which fail to consider

that the attributes of the substrate topology and virtual net-

works affect the embedding process. In this paper, for the first

time, we introduce complex network centrality analysis into

the virtual network embedding, and propose virtual network

embedding algorithms based on closeness centrality. Due to

considering of the attributes of nodes and edges in the topol-

ogy, our studies are more reasonable than existing work. In

addition, with the guidance of topology quantitative evalua-

tion, the proposed network embedding approach largely im-

proves the network utilization efficiency and decreases the

embedding complexity. We also investigate our algorithms

on real network topologies (e.g., AT&T, DFN) and random

network topologies. Experimental results demonstrate the us-

ability and capability of the proposed approach.

Keywords network virtualization, virtual network embed-

ding, complex networks, closeness centrality

1 Introduction

Solving the ossification problem of the Internet with network

Received March 26, 2012; accepted July 31, 2012

E-mail: wangzh@hpnl.ac.cn

virtualization has received a lot of attention in the past few

years [1–4]. The IP-based architecture makes the Internet

successful for deploying heterogeneous networks. Neverthe-

less, there are more and more emerging services on the In-

ternet which have different requirements that the current IP-

based Internet cannot meet. At the same time, because of the

multi-ISP environment, large-scale network innovation and

experiments cannot be tested. Many researchers have tried

to solve the problem, and a number of solutions and testbeds

have focused on network virtualization technologies [5–7].

In network virtualization environment, the traditional role

of the internet service provider (ISP) is divided into two roles:

the infrastructure provider (InP) who maintains the substrate

network, and the service provider (SP) who creates virtual

networks. SPs rent the physical resources from InPs to create

virtual networks and deploy end-to-end services to meet user

requirements. The principal advantage of network virtualiza-

tion is that multiple virtual networks will be able to coexist

on the same substrate network and offer various customized

services at the same time. For example, in network virtu-

alization environment, online games and IPTV can perform

simultaneously on different virtual networks without interfer-

ence.

Network virtualization research faces many challenges.

For example, virtual resource description, virtual network in-

stantiation, and virtual network management. The fundamen-

tal problem in network virtualization is the virtual network

embedding problem, i.e., effectively mapping the virtual net-

work requests to the substrate network with the minimum

cost of physical resources. Due to multiple objectives and

Zihou WANG et al. Topology-aware virtual network embedding based on closeness centrality 447

multiple constraints, the virtual network embedding problem

turns out to be NP-hard [3], and several heuristic algorithms

have been proposed in recent years [8–16]. Most of them

map the virtual networks in two independent phases. In the

first phase, the virtual nodes are mapped with greedy meth-

ods ignoring topology attributes. Then in the second phase,

the edges are mapped with shortest path-based algorithms.

However, separately considering the node and edge map-

ping processes will restrict the solution space, and lead to de-

creased utilization of substrate network resources and a lower

revenue of the InP. In this paper, we jointly consider the two

node and edge mapping phases by measuring the significance

of the nodes in the global network topology when mapping

the nodes in the first phase. And for the first time, we in-

troduce network centrality analysis into the virtual network

embedding problem. With the guidance of centrality anal-

ysis, we develop two novel algorithms to achieve effective

resource utilization.

In a network, even nodes with the same available re-

sources, vary in their importance due to their different loca-

tions. It is reasonable to firstly choose the substrate nodes

with the same available resources in a more important loca-

tion. Furthermore, the importance of a node is more com-

plex when the network is dynamically changing. The current

states of all the elements in the global network determine the

importance of a node. Centrality analysis provides effective

methods for measuring the importance of nodes in a com-

plex network and it has been widely used in complex network

analysis, especially in social network analysis. In the scope

of centrality analysis, the nodes can be characterized by mul-

tidimensional measures [17, 18].

To the best of our knowledge, no existing literature has ex-

plored the relationship between network centrality analysis

and the virtual network embedding problem. We map vir-

tual nodes using a fast selective algorithm based on the mea-

surement of nodes by network centrality. Different from ex-

isting solutions which map the nodes only considering local

resources, e.g., CPU and bandwidth of the adjacent edges,

we analyze the characteristics of network topology from a

global view, and take into consideration the topology prop-

erty in computing the resource availability, rather than only

resources of the nodes. The key advantage of this method is

that the virtual nodes are mapped to the more important sub-

strate nodes in a preferential manner. The importance of a

node is jointly determined by its own resources and location

in the entire topology.

The major contributions in this paper are summarized in

the following:

• Introducing network centrality to the virtual network

embedding problem. When embedding the virtual net-

works, sorting the nodes with the topology-aware close-

ness centrality method from network centrality analysis.

• Extending the closeness centrality to a new format

which is more appropriate for the virtual network em-

bedding problem. The classical definition of closeness

only considers the topology. Inspired by field theory, we

redefine closeness, which consider topology attributes

with the dynamic states of the nodes and edges at the

same time.

• Evaluating the proposed algorithms based on network

centrality. Our results show that, centrality based algo-

rithms achieve better performance. The acceptance ratio

of the two proposed algorithms is much higher than the

benchmark algorithm. The improved algorithm also de-

creases the cost of the substrate network.

In Section 2, the network model and the VN embedding

problem are formally defined. In Section 3, we introduce

network centrality to analyze the topologies of substrate net-

works and virtual networks. Two VN embedding algorithms

based on closeness are proposed in Section 4 and Section 5.

We evaluate the algorithms using experiments in Section 6.

In Section 7, we briefly review the related work. The paper

concludes in Section 8.

2 Virtual network embedding problem

In this section, we describe the general virtual network em-

bedding problem.

2.1 Network model

The substrate network topology of the InP is modeled as a

weighted graph, GS = (NS , ES ), where NS refers to the set

of nodes of the substrate network, while ES refers to the

set of edges of the substrate network. Each substrate node

nS ∈ NS is associated with an available CPU capacity value

c(nS ), while each substrate edge eS (i, j) ∈ ES between nodes

ni and n j is associated with an available bandwidth capacity

value bw(eS ).

The virtual networks of the SP are defined similarly. The

ith arriving virtual network request is denoted by GiV =

(NiV , E

iV ), where Ni

V and EiV refer to the sets of virtual nodes

and virtual edges of the ith arriving virtual network request,

respectively. Each virtual node nV ∈ NiV is associated with a

CPU requirement value c(nV) and each virtual edge eV (i, j) ∈Ei

V between nodes ni and n j is associated with a bandwidth re-

448 Front. Comput. Sci., 2013, 7(3): 446–457

quirement bw(eV). For each request, it has a lifetime td(GiV ).

If the VN request has been embedded on the substrate net-

work, the allocated resources will be dedicated to the VN

during its lifetime. When the lifetime of the VN is over, the

allocated substrate resources will be released and can be re-

allocated to other VNs.

The embedding of a virtual network refers to completely

mapping the sets of nodes and edges of a VN request GiV to

the substrate network GS . When a VN request arrives, the

InP needs to determine whether to accept it or not. If the

request is accepted, the substrate network will assign the se-

lected substrate resources to create the corresponding virtual

network. Figure 1 depicts the embedding of two VN requests

to the substrate network. Two virtual networks, Req. 1 and

Req. 2 coexist on the same substrate network. Nodes A and

B, and the edge between them are shared by the two virtual

networks. When both of the virtual networks are embedded,

the available bandwidth of edge A-B is 50−20−10 = 20 and

the available CPUs of Node A and B are 10 and 5, respec-

tively.

Fig. 1 Virtual network embedding

2.2 Objectives of virtual network embedding

The embedding problem is a multi-objective optimization

problem with multiple constraints. Researchers may focus on

different objectives. Similar to the existing methods [11, 16],

here we define the objective of VN embedding as maximiz-

ing the acceptance ratio and revenue with the same cost of

substrate network in the long term.

An important objective of VN embedding is to achieve a

high acceptance ratio of the virtual network requests over

time. In the long term, the acceptance ratio can be defined

as

limT→∞

T∑

t=0

VNRS

T∑

t=0

VNR

, (1)

where VNRS denotes the number of the virtual network re-

quests that are embedded successfully, and VNR denotes the

total number of virtual network requests.

The other two important objectives of VN embedding are

the revenue and the cost of InPs. Revenue denotes the eco-

nomic benefit of accepting VN requests. In this paper, the

revenue of an InP is described as the sum of the total virtual

resources that are embedded to the substrate network over

time. Thus, we use the following definition of revenue for a

request GiV at time t,

R(GiV , t) =

∑

e∈EiV

bw(ev) +∑

n∈NiV

c(nv), (2)

where bw(ev) and c(nv) are the bandwidth requirement of the

virtual edge e and the CPU requirement of the virtual node n,

respectively.

Our final objective is to maximize the long-term average

revenue of the InP, which is defined as:

limT→∞

T∑

t=0

R(GiV , t)

T. (3)

The cost of an InP denotes the total substrate resources al-

located to VNs. Similarly, we define the cost for a request GiV

at time t,

C(GiV , t) =

∑

p∈P(GiV )

hops(p) × bws(p,GiV) +

∑

n∈NiV

c(nv), (4)

where P(GiV) is the entire set of physical paths allocated for

virtual edges in GiV , hops(p) is the number of hops in a path

p, and bws(p,GiV) is the reserved bandwidth over a path p.

And the long-term average cost of the InP is defined as:

limT→∞

T∑

t=0

C(GiV , t)

T. (5)

If the long-term average costs of the InPs are the same, the

higher revenue is preferred. So the long-term revenue to cost

ratio is also considered to evaluate the efficiency of resource

utilization of the substrate network:

limT→∞

T∑

t=0

R(GiV , t)

T∑

t=0

C(GiV , t)

. (6)

3 Network centrality analysis

In recent years, much research focuses on complex networks.

Many real world networks that exhibit small world and free

Zihou WANG et al. Topology-aware virtual network embedding based on closeness centrality 449

scale features (WWW, Internet, ecological, cellular, etc.) are

neither totally random, nor totally regular [19,20]. Measuring

the topology attributes of real networks is essential in com-

plex network research. Centrality analysis plays an important

role in the topology analysis of complex networks. It is pro-

posed as a measure of the contribution of network position

to the importance, influence and prominence of a node in a

network. For example, how influential a person is within a

social network, or how well a road is used within an urban

network.

In the scope of graph theory and network analysis, there are

several measures of the centrality of a node within a graph

that determine the relative importance of a node within the

graph. Four measures of centrality are widely used in net-

work analysis: degree, betweenness, closeness, and eigen-

vector centrality [17,18]. These different centrality measures

reflect different attributes of the network, and lead to different

results on ranking the nodes.

• Degree centrality measures the local centrality and only

takes into account the immediate ties to neighbors that

a node has, rather than indirect ties to all others. One

node might be effected by a large number of other nodes,

which might be rather disconnected from the network as

a whole.

• Betweenness centrality reflects the switching capacity

and applies to controlling the traffic flow in the event of

congestion.

• Eigenvector centrality is mainly used to measure the

centrality of directed networks.

• A definition of node centrality on a global scale is based

on how close that the node is to all other nodes. In this

scale, the idea is that a node is central if it can quickly

reach all other nodes, not only its neighbors. That is

closeness centrality.

The closeness centrality approach emphasizes the distance

from a node to all other nodes in the network by focusing on

the distance from each node to all others. We select closeness

as the centrality measure in the VN embedding problem.

4 Algorithm based on classical closeness cen-trality

We propose two topology-aware VN embedding algorithms

in this paper. One is based on classical closeness [17] which

only takes into account the topology attributes. The other

is based on improved closeness which considers both the at-

tributes of the topology and the resources at the same time.

In the following, we present the classical notion of closeness

centrality and the corresponding algorithm. Then in the next

section, we improve the computing method of the closeness

value. The improved closeness measure involves the node

and edge resources.

4.1 Classical closeness centrality

In mathematics, closeness is one of the basic concepts in a

topological space. Intuitively we say two nodes are close

if they are arbitrarily near to each other. In network theory,

closeness is a sophisticated measure of centrality. The close-

ness of a node ni is defined as the reciprocal of the sum of

geodesic distances to all other nodes reachable from it:

Cc(ni) =1

n∑

j=1

d(i, j)

, (7)

where d(i, j) denotes the distance of the shortest path between

nodes ni and n j. If a node is near to the edge of the network,

its total distance to all reachable nodes will be large and the

closeness value will be small, and vice versa.

4.2 Detailed algorithm

The algorithm based on closeness centrality is a two-phase

VN embedding algorithm. In the first phase, the algorithm

maps the virtual nodes to the substrate nodes. Then the algo-

rithm maps the virtual edges onto the substrate edges in the

second phase.

Algorithm 1 shows the node embedding process. At the

beginning, we compute the closeness values of all nodes in

the substrate network. Then we rank the nodes according to

the values of the closeness. When a virtual network request

arrives, the algorithm will compute the closeness value for

each virtual node of the request. Then, the algorithm will

map the virtual node with the largest closeness value to the

substrate node with the largest closeness value, provided that

the CPU capacity and the edge capacity of the substrate node

can meet the virtual node requirements. The other virtual

nodes will be mapped in the same way in the order of their

closeness value. After all the virtual nodes are mapped, the

node mapping phase ends.

In the second phase, the algorithm maps the virtual edges

to the substrate edges. It adopts the edge mapping algorithm

from previous work [11, 16]. The algorithm maps the edges

with the k-shortest path algorithm which is detailed in Algo-

rithm 2. If all the virtual edges have been mapped, the entire

embedding process will be finished. The substrate network

will update the states of available resources GS and wait for

450 Front. Comput. Sci., 2013, 7(3): 446–457

Algorithm 1 Node embedding algorithm based on classical closeness

Input:

GS : current substrate network;

GiV = (Ni

V , EiV ): the ith arriving VN request;

1: begin

2: Wait until GiV arrives

3: ClosenessRank (GS );

4: ClosenessRank (GiV );

5: for all unembedded virtual nodes do

6: Choose the virtual node ni with largest closeness;

7: Map ni to substrate node that is

a. Unmapped;

b. Meets the requirement of ni;

c. Has the largest closeness;

8: if Failed to map ni then

9: return failure;

10: end if

11: end for

12: return success;

13: end

Algorithm 2 Edge mapping algorithm

Input:

EiV : The set of virtual edges;

ES : The set of substrate edges;

1: begin

2: for eV (i, j) ∈ EiV do

3: while k > 0 do

4: k=1;

5: Find the k-shortest path pS (i, j) ∈ ES between nodes i and j;

6: if (No k-shortest path pS (i, j)) then

7: return failure;

8: else if bw(eV (i, j)) � bw(pS (i, j)) then

9: Embed(eV (i, j), pS (i, j));

10: break;

11: else

12: k++;

13: end if

14: end while

15: end for

16: return success.

17: end

new VN requests.

5 Algorithm based on improved closeness

The classical definition of closeness is only concerned with

the topology attributes, and does not include the capacities

and states of nodes and edges. This model is not sufficient for

VN embedding scenarios. First, substrate networks and vir-

tual networks are weighted networks, and classical closeness

does not consider the weights of nodes and edges. Second,

computing results of classical definition are static, and can-

not respond to the dynamically changing states of nodes and

edges. In fact, in the context of virtual network embedding,

the constraints of nodes and edges are essential. Hence, we

extend the definition of the closeness with attributes of nodes

and edges, which was inspired by field theory in physics [21].

5.1 Improved closeness for VN embedding

In field theory, a network G is proposed as a physical system

including n nodes [21, 22]. Each node in a field influences

other nodes in the same field and is also effected by other

nodes. The effect of the node will decrease quickly with

the increasing distance. In the literature [21], researchers

describe the interaction in a Gaussian function. Given G =

(N, E), where N is the set of nodes and E is the set of edges.

The potential in the field φ of the node ni is defined as:

φ(ni) =n∑

j=1

m j × e−( d(i, j)δ )2, (8)

where d(i, j) denotes the distance between nodes ni and n j,

δ denotes the influence range of nodes, m j � 0 denotes the

mass of the nodes; these are regarded as a natural attributes

of the nodes. In real networks, the natural attributes of nodes

may be the scale of the city in urban networks, the individ-

ual ability in social networks, and the storage of the nodes in

communication networks.

In the virtual network embedding problem, the main at-

tributes in networks are the processing capacity of nodes, the

bandwidth of edges, and the distances between nodes. We

use the Gaussian function to describe the improved closeness

to solve the virtual network embedding problem:

P(ni) =n∑

j=1

c(n j) × e−( d(i, j)MinBW(i, j) )2

, (9)

where P(ni) denotes the improved closeness with resource at-

tributes, c(n j) denotes the processing capacity of the node

n j, d(i, j) denotes the distance between nodes ni and n j,

MinBW(i, j) denotes the influence range of the node, and here

it is described as the available bandwidth on the shortest path

between nodes ni and n j. Along the shortest path between

nodes ni and n j, the available bandwidth is different in dif-

ferent segments, and we choose the segment with the mini-

mum bandwidth as the metric. The segments are cascaded

in series, thus the available bandwidth of the shortest path is

determined by the segment with the minimum bandwidth.

This new expression of closeness is advantageous in con-

sidering the attributes of nodes and edges. The significance

Zihou WANG et al. Topology-aware virtual network embedding based on closeness centrality 451

of a node is jointly determined by its own resources, other

nodes’ resources, and the distances to all the other nodes.

The improved closeness adapts to the constantly changing

networks.

The classical closeness values of nodes are static and only

need to be computed once while the improved closeness val-

ues of nodes which require real-time update are computed

every time the VN request arrives.

5.2 Time complexity analysis

Computing classical closeness and improved closeness of

all nodes in a graph involves calculating the shortest paths

between all pairs of nodes. The time complexity is deter-

mined by the number of nodes and edges. Both of the algo-

rithms take time O(N2 lg N +NE), where N and E denote the

numbers of nodes and edges in the graph, respectively [23].

The k-shortest algorithm can be solved in polynomial time

O(N + E) [24]. The time complexity of the two novel algo-

rithms is affordable.

6 Experimental evaluation

Our evaluation focuses on quantifying the advantages of im-

proving the node mapping phase in terms of acceptance ratio,

average revenue, cost, and revenue to cost ratio in the long

term, similar to the existing literature [9–16]. The experiment

results show that, compared with a baseline algorithm, the al-

gorithm based on classical closeness increase the acceptance

ratio of InPs, and the algorithm based on improved close-

ness highly increase the substrate resource utilization while

increasing the acceptance ratio.

6.1 Simulation environment

We implemented a discrete event simulator to evaluate the

performance of our algorithms. In the existing literature

[9–16], substrate network topologies are generated as random

graphs, which are not sufficient to reflect real networks. In

our experiments, we perform two group simulations on two

different kinds of network topology. In the first group we

generate the substrate network topology randomly in order

to provide fair comparison with existing algorithms. In the

second group we will perform the algorithms on real network

topologies.

We use GT-ITM tool [25] to generate substrate and virtual

networks. The CPU and bandwidth resources of substrate

nodes and edges are real numbers uniformly distributed be-

tween 50 and 100. We assume that the VN requests arrive

as a Poisson process with an average rate of five requests per

100 time units. Each request has an exponentially distributed

lifetime td with a mean of 1 000 time units. In each VN re-

quest, the number of virtual nodes is randomly determined

by a uniform distribution between 2 and 10. Each pair of

nodes is randomly connected with probability 0.5. The CPU

and bandwidth requirements are real numbers uniformly dis-

tributed between 0 and 50. We run all of our simulations for

50 000 time units, corresponding to about 2 500 VN requests

on average in one instance. This is sufficient to get the simu-

lation data towards a steady state.

Here we compare the two proposed algorithms (classical

closeness, CL; improved closeness, IC). Our evaluation fo-

cuses primarily on quantifying the benefits of centrality anal-

ysis and topology-aware node ranking. We implement the

algorithm in [11] as the baseline (denoted by Greedy). The

baseline algorithm takes the available node resources as the

rank of the node. The three algorithms, Greedy, CL and IC,

consider local resources, topology attributes, and both, re-

spectively. The notations that we use to refer to different al-

gorithms are enumerated in Table 1.

Table 1 Algorithms in comparison

Notation Description

Greedy The traditional greedy algorithm as the baseline, includinggreedy node/edge mapping

CL The algorithm with node ranking based on classical closenesscentrality considering the topology

IC The algorithm with node ranking based on improved closenesscentrality considering both the topology and the resources

6.2 Performance on random topologies

In the first group of our experiments, the substrate network

topology is randomly generated with 100 nodes, and about

500 edges, similar to a mid-size ISP. Here we use perfor-

mance metrics as presented in Section 2 to evaluate the al-

gorithms we have proposed.

Figure 2 shows the simulation results in the first group.

Figure 2(a) shows the acceptance ratio of the three algo-

rithms. After about 10 000 time units, the experiment reaches

an approximately steady state. The acceptance ratio of two

algorithms based on closeness (CL: 0.90, IC: 0.88) is about

0.10–0.12 higher than the acceptance ratio of the greedy algo-

rithm (0.78–0.80). The closeness measurement, with consid-

eration of topology information, can improve the acceptance

ratio of mapping results effectively. When the substrate net-

work is random, the acceptance ratio of CL is slightly higher

(0.02) than that of IC. This is for the reason that when the

graph is dense and uniformly distributed, the embedding has

452 Front. Comput. Sci., 2013, 7(3): 446–457

Fig. 2 Performance comparison, on random topologies. (a) Acceptance ratio changes with time; (b) the long-term Revenue changes withtime; (c) the long-term cost changes with time; (d) the long-term revenue/cost ratio changes with time

sufficient alternative resources, and the resources are less im-

portant in measuring the significance of the node. Hence, the

classical closeness without parameters can perform better in

the aspect of acceptance ratio.

Figure 2(b) depicts the revenue of different algorithms. CL

and IC, lead to higher revenue than the greedy algorithm. Fig-

ure 2(c) shows the long-term average provisioning cost of the

substrate network. When the algorithm increases the revenue

and acceptance ratio, it also increases the cost of the substrate

network, so does CL and IC. Figure 2(d) shows the revenue to

cost ratio. From Figs. 2(b), 2(c), and 2(d), we can see that the

IC algorithm increases the revenue while decreasing the cost.

The IC (R/C: 0.64) increases the resource utilization by about

5% than the CL (R/C: 0.61). Comparing IC with CL, having

higher revenue/cost ratio along with nearly the same accep-

tance ratio implies that IC algorithm actually embed VN re-

quests that generate higher revenue, instead of just small VN

requests. And it reflects that the IC algorithm maps the vir-

tual resources of the VN requests in a more concentrated form

which decreases the cost of the substrate resources. The im-

proved closeness helps to cut down the energy consumption.

6.3 Performance on real network topologies

In the second experiment, we adopt two real network topolo-

gies as the substrate network topology, the AT&T network

and the DFN network [26], which are illustrated in Fig. 3.

The AT&T network topology has 154 nodes with about 200

edges. The DFN network topology has 30 nodes with about

50 edges. The real topologies are sparser than the random

graph used in the previous section. Other settings in the ex-

periments are the same as in the previous experiment. Results

of the simulations are shown in the Fig. 4.

Fig. 3 The DFN and AT&T topologies

Figures 4(a) and 4(c) show that, the acceptance ratio of

all the algorithms are lower than in the random network of

the first experiment, however, the proposed algorithms per-

form much better. With the DFN topology, the IC algorithm

(0.24) increases the acceptance ratio by 0.06 and 0.02 over

the baseline algorithm (0.18) and CL algorithm (0.22), re-

spectively. With the AT&T topology, the acceptance ratio of

the baseline, CL, and IC algorithms are 0.16, 0.21, and 0.25,

respectively. When the network is sparse, network central-

ity obtains a more accurate global ranking that can reflect the

importance of nodes in the network.

From Figs. 4(b) and 4(d) we can see, the revenue to cost

ratio of the proposed algorithms is higher than the baseline

algorithm. With the DFN topology, the IC algorithm (0.63)

Zihou WANG et al. Topology-aware virtual network embedding based on closeness centrality 453

Fig. 4 Performance comparison, on real network topologies. (a) Acceptance ratio with DFN topology; (b) the long-term revenue/cost ratiowith DFN topology; (c) acceptance ratio with AT&T topology; (d) the long-term revenue/cost ratio with AT&T topology

increase the revenue/cost ratio by 14% than the baseline algo-

rithm (0.55), and by 8% than the CL algorithm (0.58). With

the AT&T topology, the revenue/cost ratio of the baseline,

CL, IC is 0.45, 0.5, and 0.6, respectively. The results shows

that the proposed algorithms have better revenue/cost ratio

when the substrate networks have a real topology. And the

IC algorithm has a better efficiency in increasing the revenue

while decreasing the cost of physical resources.

6.4 Acceptance ratio with different kinds of VNs

In real networks, applications vary in their requirements in

the types of required resources. Some applications may re-

quire more node resources, for example, P2P content cache

system, while other applications require more edge resources,

for example, IPTV and VoIP. To further evaluate the perfor-

mance of the proposed algorithms, in Fig. 5, we have tested

Fig. 5 Acceptance ratio changes with different kinds of requirements. (a) Acceptance ratio changes with scales of VNs; (b) acceptance ratiochanges with connectivity of VNs; (c) acceptance ratio changes with CPU; (d) acceptance ratio changes with bandwidth

454 Front. Comput. Sci., 2013, 7(3): 446–457

Table 2 Different kinds of VNs

Variable Description

Scale The VNs require more virtual nodes

Connectivity The VNs require more connectivity between virtualnodes

Larger Nodes The VNs require more node resources

Larger Edges The VNs require more edge resources

different types of virtual networks with the random substrate

networks while keeping other parameters the same. The situ-

ations are described in Table 2.

Figure 5(a) examines the benefits of the proposed algo-

rithms for larger virtual networks. The number of virtual

nodes in each virtual network uniformly ranges between 2

and x, where x represents the variable on X-axis [5, 40]. The

probability of a pair of nodes being connected is 0.5. We

can see that, when the number of virtual nodes increases, the

performance of all the three algorithms decreases. But the

proposed algorithms still have a relatively higher acceptance

ratio (CL: 4–5%, IC:6–8%) than the baseline algorithm. Our

algorithms are effective when the virtual network needs more

virtual nodes.

Figure 5(b) shows the performance of different algorithms

when the connectivity probability of the virtual network in-

creases from 0.1 to 1.0. When the connectivity probability is

1.0, the virtual network is a complete graph. When the vir-

tual network requires more connectivity, i.e., more edges, the

performance of all the three algorithms will decrease. The

proposed algorithms have better performance (about 5%–

10%) than the baseline algorithm. Comparing Figs. 5(a) and

5(b), an interesting result shows that the number of nodes

has greater influence on the performance than the edges. The

curves in Fig. 5(a) decrease more steeply than the curves in

Fig. 5(b).

Next, we will discuss the acceptance ratio changes with

the scale of the virtual nodes and edges. Here we present the

performance of the algorithms with the increasing node and

edge resource requirements. Firstly, we uniformly distribute

the CPU requirements between 0 and x (variable on X-axis

[20, 80] in Fig. 5(c)) while the bandwidth requirements are

between 0 and 50. Fig. 5(c) depicts the acceptance ratio of

the three algorithms as the required node resources increase.

When the VN requests ask for more node resources (x > 40),

the two closeness-based algorithms perform better than the

baseline algorithm though performances of all the algorithms

decreases.

The bandwidth requirements are real numbers uniformly

distributed between 0 and x (variable on X-axis [20, 80] in

Fig. 5(d)) while CPU requirements are uniformly distributed

between 0 and 50. Fig. 5(d) shows the acceptance ratio of

the three algorithms with the increasing required edge re-

sources. Performance of all the algorithms decreases when

more edge resources are required. Nevertheless, the perfor-

mance of closeness-based algorithms have a higher accep-

tance ratio in a greater range (20 < x < 60). When the virtual

network requires more larger edges (x > 60), the difference

in performance is no longer obvious.

The above results demonstrate that our proposed algo-

rithms are effective and flexible when the requirement of vir-

tual networks changes.

6.5 Acceptance ratio with different substrate networks

We also consider the performance of algorithms with differ-

ent scales of substrate networks. Figure 6 shows the changing

acceptance ratio with increasing substrate nodes [60, 200].

Generally, the acceptance ratio will increase when the sub-

strate network has more nodes. The two proposed algorithms

have higher acceptance ratio than the basic greedy algorithm

when the nodes are not enough (number of substrate nodes

< 160).

Fig. 6 Acceptance ratio with different substrate networks

7 Related work

7.1 Network virtualization

In recent years, many researchers have focused on network

virtualization. CABO [27] promised separation between in-

frastructure providers and service providers, and allowed ser-

vice providers to simultaneously run multiple end-to-end ser-

vices over a substrate network owned by different infras-

tructure providers. Cabernet [28] introduced the connectiv-

ity layer, and used virtual edges purchased from infrastruc-

ture providers to run virtual networks with the necessary ge-

Zihou WANG et al. Topology-aware virtual network embedding based on closeness centrality 455

ographic footprint, reliability, and performance for the ser-

vice providers. The Global Environment for Network Inno-

vations (GENI) [6] is to build an open, large-scale, realis-

tic experimental facility for evaluating new network architec-

tures. GENI promises virtualization in the form of slices of

resources in space and time. 4WARD virtualization frame-

work [7] provides virtualization of heterogeneous network-

ing technologies and coexistence of multiple networks on

a common platform through carrier-grade virtualization of

networking resources. SecondNet [4] proposed a data cen-

ter network virtualization architecture which is applicable to

arbitrary network topologies using commodity servers and

switches. Lemay et al. proposed a solution for converging

of cloud computing and network virtualization, for a better

energy efficiency [29]. Khan et al. argue that network virtu-

alization provides a way of organizing networks [30].

7.2 Virtual network embedding

The VN embedding problem is similar to previous work in

embedding virtual private networks (VPN) to ISP networks.

In VPN embedding, only edge mapping needs to be consid-

ered [31, 32]. However, in a network virtualization environ-

ment, the VN embedding problem must deal with both node

and edge constraints for arbitrary topologies.

Even if some of the constraints are ignored, the VN em-

bedding problem is computationally hard. Researchers have

only considered the problem by restricting the problem space

in one or more dimensions and provided heuristic algorithms.

A VN embedding algorithm based on simulated annealing

was proposed in [8], and they only consider the bandwidth

constraints. Lu and Turner developed an embedding method

in a cost-efficient way [9]. Zhu and Ammar assign virtual

nodes and virtual edges to the substrate network based on

greedy algorithms and shortest path algorithms [10]. Yu et

al. assume the substrate network to be supportive to split

the virtual edges into different substrate paths, and adopt

multi-commodity flow algorithms (MCF) to embed the vir-

tual edges [11]. However, the above works focus on the off-

line problem, where all the requests are known in advance.

Chowdhury et al. proposed VN embedding algorithms based

on linear programming and rounding to solve the location-

based embedding [12]. Lischka and Karl proposed an al-

gorithm based on subgraph isomorphism detection while re-

stricting the length of substrate paths [13]. Based on Chowd-

hury’s method, Houidi et al. proposed an inter-domain al-

gorithm that maps virtual nodes and virtual edges to multi-

ple providers without a centralized controller but has poor

performance [14]. Zhang et al. proposed an opportunistic

bandwidth sharing method in the same physical link among

multiple virtual links from different VNs [15]. Cheng et al.

proposed VN embedding algorithms based on Markov Ran-

dom Walk that considers the adjacent available resources of

the nodes when mapping nodes [16]. Botero et al. extended

the virtual network embedding problem to energy awareness

and proposed an algorithm which provides optimal energy

efficient embeddings [33].

With the exception of Cheng et al., all previous work stud-

ied the problem without considering the network topology. In

Cheng et al.’s method, there may be many different eigenval-

ues for which a solution exists. The artificially fixed eigen-

value is unable to adapt to a dynamic network environment.

8 Conclusion

Virtual network embedding is essential in network virtual-

ization. In this paper, we have proposed two novel algo-

rithms for VN embedding that differ from existing algo-

rithms; our algorithms introduce network centrality to ana-

lyze the topologies and enhance the collaboration of node

mapping and edge mapping phases. We redefine the close-

ness centrality using field theory. Our theoretical analysis and

experimental results on random and real-world networks in-

dicate that our proposed algorithms based on classical close-

ness and improved closeness increase the acceptance ratio

and the revenue while decreasing the cost incurred by the

substrate network.

There are still a number of issues that remain unresolved.

The analysis of the paper is still confined to the context of

an intra-domain environment. We are currently working on

embedding algorithms in an inter-domain environment. The

consideration of other attributes of the substrate and virtual

networks is another important issue that needs attention, e.g.,

the substrate location constraints of embedded virtual nodes,

or the pricing of substrate network resources. We are also

exploring a general VN embedding framework involving

multiple constraints.

Acknowledgements This work has been supported by National Scienceand Technology Major Project of China (NMP) (2010ZX03004-002 and2012ZX03003-003), the Strategic Pilot Project of Chinese Academy of Sci-ences (XDA06010302), and the National Natural Science Foundation ofChina (Grant No. 60972083).

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Zihou Wang received his BSc in elec-

tronics from Peking University, China,

in 2008. Now he is a PhD candidate in

the High Performance Network Labo-

ratory at the Institute of Acoustics, Chi-

nese Academy of Sciences. His main

research interests are in the areas of

complex network optimization, future

Internet design, and network virtualization.

Yanni Han is an assistant researcher

with the Institute of Acoustics, Chi-

nese Academy of Sciences. Her cur-

rent research interests include cognitive

networks and virtual network manage-

ment.

Zihou WANG et al. Topology-aware virtual network embedding based on closeness centrality 457

Tao Lin is an associate researcher

with the Institute of Acoustics, Chinese

Academy of Sciences. His current re-

search interests focus on network archi-

tecture design and content-centric net-

works.

Yuemei Xu received her BSc in com-

munication engineering from Beijing

University of Posts and Telecommuni-

cations, China, in 2009. She is cur-

rently a PhD candidate with the Insti-

tute of Acoustics, Chinese Academy of

Sciences. Her current research inter-

ests focus on service computing and

content-centric networks.

Song Ci is a professor with the Insti-

tute of Acoustics, Chinese Academy of

Sciences. He is also an associate pro-

fessor in the Department of Electron-

ics and Engineering at the University

of Nebraska-Lincoln, USA. He is the

director of the Intelligent Ubiquitous

Computing Lab (iUbiComp Lab) and holds a courtesy appointment

of UNL PhD in the Biomedical Engineering Program. His re-

search interests include dynamic complex system modeling and op-

timization, green computing and power management, content-aware

quality-driven cross-layer optimized multimedia over wireless net-

works, and cognitive network management.

Hui Tang is a professor with the In-

stitute of Acoustics, Chinese Academy

of Sciences. His research interests in-

clude next generation Internet, wire-

less multimedia technologies, Internet

of things, mobile Internet, and P2P

technologies.