Constructing Minimum Energy Mobile Wireless networks

1
Constructing Minimum Energy Mobile Wireless
networks

• Xian-Yang Li and Peng-Jun Wan
• ACM SIGMOBILE
• Mobile Computing and Communications Review, 2001

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Outline

• Introduction
• Preliminaries
• Without receiver cost
• Centralized algorithm
• Distributed algorithm
• Dynamic distributed networks
• Conclusion

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Introduction

• Energy conservation is a critical issue in
  wireless ad hoc networks.
• It may be efficient to use another node to relay
  the signal sent from u to v.
• A central challenge is to find energy-efficient
  routes between two communication nodes.
• The minimum-power path can be easily found by
  some shortest path algorithm when the global
  information of nodes is available
• If global information is not available, the
  minimum-power path can be found by some protocols
  based on the flooding approach.

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• Thus is desired a distributed and localized
  protocol that constructs a spare topology to
  alleviate the redundant overhead caused by
  flooding message.
• The spare topology should contains the minimum-
  power path between all pair of nodes

Original topology
Spare topology
Minimum-power topology
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• Rodoplu and Meng described a protocol that has
  time complexity O(dGt(u)3) and space complexity
  O(dGt(u)2) on each node u.
• The proposed protocols has time and space
  complexities much less than the previous one.
• Each node u, instead of finding nodes that can
  not be served a relay nodes, tries to find the
  nodes that are guaranteed to be the neighbors of
  u.

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Preliminaries

• Energy consumption models
• uva, a 2
• uva c, a 2, c gt 0
• uva, agt 2
• uva c, agt 2, c gt 0
• Transmission graph a wireless networks can be
  modeled as a weighted directed graph Gt(V, E)
• (u, v)?E if node v is in the transmission range
  of u
• The weight of (u, v) is the power consumed for
  transmitting from u to v
• Unit disk graph all nodes have the same
  transmission range

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• Each mobile node can adjust the transmission
  power
• Each node has a lower-power GPS receiver, which
  provides the position information of node itself.
  

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• Relay region

a 2
agt 2
R2,c(s,r)
Ra,c(s,r)
sr/2
sr/2
The boundary of relay region
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s
r
sra rda lt sda
d
A node d is not in the realy region R(s,r) does
not imply that node r will not relay the signal
to d
A node d is in the relay region R(s,r) does not
imply that r has to relay signal to d
s
r
s
r
r
x
d
d
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• Given two nodes s and r, the relay region
  Ra1(s,r) ? Ra2(s,r) if
• a1lta2 and
• c 0 or c ? 1

s
s
r
r
R2(s,r)
R2(s,r)
R4(s,r)
R4(s,r)
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• Enclosure region of s

Neighbors of node s p1, p2, p3, p4, p5
pmax
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• Enclosure graph
• The concatenation of the edges in all nodes
• If the original topology is strongly connected,
  the enclosure graph is also strongly connected.
• The enclosure graph contains the minimum- power
  topology

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• The enclosure graph is not loop-free

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• The degree of a node in its enclosure region is
  not bounded

• However the average degree of a node in its
  enclosure region is bounded.

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Without receiver cost

• Voronoi diagram
• Delaunay triangulation
• The nodes connected to node u in enclosure graph
  is a subset of nodes connected to u in Delaunay
  triangulation
• The average number of degree in a Delaunay
  triangulation is bounded
• the average number of degree in an enclosure
  graph is bounded
• Delaunay triangulation is a planer graph
• enclosure graph is a planer graph
• The shortest path in planer graph can be found in
  linear time

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• Voronoi diagram for any vertex, very point in
  the region of the vertex is closer to that vertex
  than any others

• the Voronoi diagram of a n node graph can be
  constructed in O(nlong) steps by a centralized
  algorithm

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• Delaunay triangulation the dual of Voronoi
  diagram

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• The circumcircle of each of its triangles does
  not contain any nodes

u
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• The nodes connected to node u in enclosure graph
  is a subset of nodes connected to u in Delaunay
  triangulation for a?2 and c 0

v
w
u
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• Delaunay triangulation is a planer graph
• Enclosure graph is a planer graph
• The number of edges in a planer graph is at most
  3n-6
• The number of edges in an enclosure graph is at
  most 3n
• The average number of degree in an enclosure
  graph is at most 6

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Centralized algorithm

• A simple centralized method extended from a
  localized algorithm in literature
• For each node u
• For each node v
• Compute R(u, v)
• For each node k in the enclosure graph of u
• Combine R(u, v) with R(u, k) to shrike the
  enclosure of u
• The time complexity is O(n3)

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• The proposed centralized algorithm
• compute a Delaunay triangulation O(nlogn)
• Eliminate the Delaunay neighbors of node u that
  are in the relay region of other node in node u
  O(n)
• The time complexity is O(nlogn)
• The minimum energy path can be found in O(n) by a
  fast shortest path algorithm for planer graph

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Distributed algorithms

• Step 1 construct a voronoi region for u

u
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Distributed algorithms

• The corresponding Delaunay triangulation

u
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• Step 2 construct the enclosure region of u

u
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• The corresponding neighbors of u

u
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• Comparison

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Dynamic Distributed Networks

• A node moves from one position to other position
  can be viewed as two events
• One node is deactivated at the old position
• One node is activated at the new position
• Add a new node z
• Node z broadcasts its position to nearby nodes
• Only some node u whose enclosure region contains
  z need to be updated
• Remove each neighbor v of u if v ? R(u, z)

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• Remove an node z
• Node z broadcasts its position to nearby nodes
• Only some node u whose enclosure region contains
  z need to be updated
• Revive each non-neighbor v of u if v ? R(u, z)

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Conclusion

• Described a distributed protocol to find an
  enclosure graph that approximates the minimum
  power topology for a stationary wireless ad hoc
  network
• Further works
• Develop an algorithm which can directly find the
  shortest path or find the path whose length is
  within a constant factor of the shortest path

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The END