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8/2/2019 Topology Control in Heterogeneous Wireless Networks
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Topology Control in HeterogeneousWireless Networks: Problem and Solution
Ning Li and Jennifer C.HouDepartment of Computer Science
University of Illinous at Urbana-Champaign
08.03.29
System Software LaboratoryMyung-Ho Kim TeamDae-Woong JO
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Contents
Introduction
Network Model
Related Work and Why They Cannot Be DirectlyApplied To Heterogeneous Networks
DRNG and DLMST
Properties Of DRNG and DLMST
Simulation Study
Conclusions
References
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Introduction
Energy efficiency and Network capacity Reducing Energy consumption and improving network capacity
Two localized topology control algorithms
DRNG Directed Relative Neighborhood Graph
DLMST Directed Local Minimum Spanning Tree
Be able to prove
1) Derived under both DRNG and DLMST
2) DLMST is bounded, DRNG may be unbounded.
3) DRNG and DLMST preservers network bi-directionality
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Introduction (cont.)
Simulation results indicate Compared with the other known topology control algorithms
Have smaller average node degree (both logical and physical)
Have smaller average link length.
In Section 2 Network model
In Section 3 Summarize previous work on topology control
In Section 4 DRNG and DLMST algorithms
In Section 5 Prove several of their useful properties
In Section 6 Evaluate the performance of the proposed algorithms
In Section 7 conclude
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Network Model
V = {v1, v2, . . . , vn}, random distrivuted in the 2-Dplane.
Let rvi Maximal transmission range of vi
Heterogeneous network All nodes may not be the same.
rmin= minv
V {rv} rmax= maxvV {rv}
d(u,v) is distance between node u and node v
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Network Model (cont.)
Simple directed graph G = (V(G),E(G)) V(G) = randomly distributed in the 2-D plane E(G) = {(u,v) : d(u,v) w(u2, v2)
d(u1, v1) > d(u2, v2)
or (d(u1, v1) = d(u2, v2)
&&max{id(u1), id(v1)} > max{id(u2), id(v2)})
or (d(u1, v1) = d(u2, v2)&&max{id(u1), id(v1)} = max{id(u2), id(v2)}
&&min{id(u1), id(v1)} > min{id(u2), id(v2)}).
Definition 3 (Neighbor Set ) Algorithm A, denoted u
A v
NA(u) = {vV (G) : uA
v }.
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Network Model (cont.)
Definition 4 Topology
Directed graph GA = (E(GA),V(GA)) Where V (GA) = V (G), E(GA) = {(u, v) : u
A v , u, vV (GA)}.
Definition 5
Radius The radius, ru, of node u is defined
Definition 6 Connectivity
Topology generated by an algorithm A Node u is connected to node v (denoted uv)
If there exists a path(p0 =u, p1,,pm-1,pm= v) It follows that u => v if u = > p and p = > v for some pV(GA)
Definition 7 Bi-Directionality
Any two nodes u,v V (GA), uNA(v) implies vNA(u).
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Network Model (cont.)
Definition 8 Bi-Directional Connectivity
Bi-directionally connected to node v (denoted uv) If there exists a path p0 = u, p1,pm-1, pm = v) It follows that u u if u p and p v for some p V(GA)
Definition 9
Addition and Removal
Addition operation
extra edge (v, u) E(GA)
Removal operation delete any edge (u, v) E(GA)
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RELATED WORK AND WHY THEY CANNOT BEDIRECTLY APPLIED TO HETEROGENEOUS NETWORKS
System Software Laboratory
Ramanathan et al. [5] Two distrubuted heuristics for mobile networks
Require global information
Cannot be directly deployed
Borbash and Jennings [8] Proposed to use RNG
(Relative Neighborhood Graph)
Topology initialization of wireless networks
Good overall performance
Low interference, and reliablity
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RELATED WORK AND WHY THEY CANNOT BEDIRECTLY APPLIED TO HETEROGENEOUS NETWORKS
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Definition 10 ( Neighbor Relation in RNG) u
RNG v if and only if there does not exist a third
node p such thatw(u, p) < w(u, v) and w(p, v) < w(u, v).
Or equivalently, there is no node
inside the shaded area
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RELATED WORK AND WHY THEY CANNOT BEDIRECTLY APPLIED TO HETEROGENEOUS NETWORKS (cont.)
System Software Laboratory
CBTC() [6] Proved to preserve network connectivity
In [10] Proposed LMST(Local Minimum Spanning Tree)
Topology control in homogeneous wireless multihop- networks
Proved thatLMST preserves the network connectivity
The node degree of any node
Can be transformed into one with bi-directional links
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RELATED WORK AND WHY THEY CANNOT BEDIRECTLY APPLIED TO HETEROGENEOUS NETWORKS (cont.)
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DRNG and DLMST
Propose two localized topology control algorithms DRNG (Directed Relative Neighborhood Grpah)
DLMST (Directed Local Minimum Spanning Tree)
Both algorithms are composed of three pahses Information Collection
Topology Construction
Construction of Topology with only Bi-Directional Links
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DRNG and DLMST (cont.)
Definition 12 Neighbor Relation in DRNG
uDRNG
v if andonly if d(u, v) ruand there does not exist a third node p
such that w(u, p) < w(u, v) and w(p, v) < w(u, v), d(p, v) rp
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DRNG and DLMST (cont.)
Definition 13 Neighbor Relation in DLMST
Directed Local Minimum Spanning TreeGraph (DLMST)
uDLMST
v if and only if (u, v) E(Tu), where Tu is thedirected local MSTrooted at u that spans N
R
u.
each node u computes a directed MST that spans NR
uand takes on-tree
nodes that are one hop away as its neighbors
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Properties of DRNG and DLMST
Discuss the connectivity, bi-directionality anddegree bound of DLMST and DRNG
Connectivity
Theorem 1 (Connectivity of DLMST) If G is strongly connected, then G DLMST is also strongly connected.
Proof For any two nodes u, vV (G), there existsa unique global MST T
rooted at u since G is stronglyconnected. Since E(T) E(GDLMST)by Lemma 2, thereis a path from u to v in GDLMST.
Lemma 2 : Let T be the global directed MST of G rooted at any node w V(G) ,then E(T) E(Gdlmst)
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Properties of DRNG and DLMST
Theorem 2 (Connectivity of DRNG) If G is strongly connected, then G DRNG is also strongly connected.
Proof For any two nodes u, vV (G), since G is strongly connected, there
exists a path (p0 = u, p1, p2, . . . , pm1, pm = v) from u to v, such
that(pi, pi+1) E(G), i = 0, 1, . . .,m 1. Thus pipi+1 in GDRNGbyLemma 3. Therefore, uv in GDRNG. Hencewe can conclude thatGDRNGis strongly connected.
Lemma 3: For any edge (u,v) E(G), we have u => v in Gdrng
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Properties of DRNG and DLMST (Cont.)
Bi-directionality Theorem 3
If the original topology G is strongly connected and bi-directional,then G DLMST and G DRNG are also strongly connected and bi-directional
Proof For any two nodes u, vV (G), there exists atleast one path p =
(w0 = u,w1, w2, , wm1, wm = v)from u to v, where (wi, wi+1) E(G), i = 0, 1, ,m 1. Since wiwi+1 in GDLMSTby Lemma 5,we have uvin GDLMST. Therefore, wiwi+1 in GDRNG, whichmeans uv in GDRNG. The same results still hold after Addition or
Removal
Lemma 5 : If the original topology G is strongly connected and bi-directional, then any edge (u,v) E(G) satisfies that u v in Gdlmst
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Properties of DRNG and DLMST(Cont.)
Degree Bound Theorem 4
For any node uV (GDLMST), the numberof neighbors in GDLMSTthat are inside Disk(u, rmin) is atmost 6.
Theorem 5 The out degree of node in GDLMST is boundedby a constant that
depends only on rmaxand rmin.
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Simulation Study
Evaluate the performance R&M, DRNG and DLMST by simulations.
Preserve network connectvity in heterogeneousnetworks
First simulation 50 nodes are uniformly distributed
1000m x 1000m region
R&M, DRNG and LMST all reduce
Average node degree, while maintaining network connectivity
DRNG and DLMST outperforms R&M
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Simulation Study (cont.)
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Simulation Study(cont.)
Second simulation Vary the number of nodes in the region
80 to 300
Average of 100 simulation runs
Each data point Nodes are uniformly distributed in [10m,250m]
Average radius and the average edge length
NONE(no topology control)
R&M, DRNG, and DLMST
DLMST outperforms the others
Better spatial reuse and use less energy
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Simulation Study (cont.)
Compare the out degree The topologies by different algorithms
The result of NONE is not shown
Langer than under R&M, DRNG, DLMST
Out degrees increase linearly
Shows the average logical/physical
Derived by R&M, DRNG, DLMST
Under R&M and DRNG increase
Under DLMST actually decrease
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Simulation Study (cont.)
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Conclusions
Proposed two local topology control algorithms DRNG, DLMST
Heterogeneous wireless multi-hop networks
Have different transmission ranges
Show that
Most existing topology control algorithms
Have different transmission ranges
Disconnected network topology
Directly applied to heterogeneous networks.
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Conclusions(cont.)
DRNG and DLMST prove1) Preserve network connectivity
2) Preserve network bi-directionality
3) Bounded in the topology under DLMST ,Unbounded
under DRNG
Future research
Different maximal transmission power
Density of nodes, distribution of the transmission ranges
MAC-level interference affect network
Connectivity and bi-directionality
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References (cont.)
[8] S. A. Borbash and E. H. Jennings, Distributed topology control algorithm for multihop wireless
networks, in Proc. 2002 World Congress onComputational Intelligence (WCCI 2002), Honolulu, Hawaii, US, May2002.
[9] X.-Y. Li, G. Calinescu, and P.-J. Wan, Distributed construction of planar
spanner and routing for ad hoc networks, in Proc. IEEE INFOCOM
2002, New York, New York, US, June 2002.
[10] N. Li, J. C. Hou, and L. Sha, Design and analysis of an MSTbasedtopology control algorithm, in Proc. IEEE INFOCOM 2003, San
Francisco, California, US, Apr. 2003.