Minimum Energy Disjoint Path Routing in Wireless Adhoc Networks by Anand Srinivas, Eytan Modiano

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Minimum Energy Disjoint Path Routing in Wireless
Ad-hoc Networksby Anand Srinivas, Eytan Modiano

• Oct.14.2004
• presented by
• JISU LIM

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Contents

• Introduction
• Network Model
• Minimum Energy Node-Disjoint Paths
• Source Transmit Power Selection (STPS) Algorithm
• Minimum Energy Link-Disjoint Paths
• Optimal Common Node Decomposition (OCND)
  Algorithm
• Lower Complexity Heuristics
• Results
• Conclusion

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Introduction Reliability

• The need for reliability in wireless networks
• Node disjoint path
• More reliable
• Link disjoint path
• More energy efficient

2 Link disjoin path
2 Node disjoint path
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Introduction Energy Efficiency

• The importance of energy efficiency in wireless
  networks
• Joint consideration of the network and physical
  layer issue
• K-disjoint paths between source and destination

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Network Model

• Energy cost graph
• Given a network of N nodes and co-ordinates for
  each node, construct a graph G (V,E) such that
  (i, j) ? E ?? raij Emax and wij raij (where
  wij is the weight of link (i, j), raij is the
  power required to support a wireless link at a
  given data rate)

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Network Model

• Wireless Multicast Advantage (WMA)
• Transmission is simultaneously received by all
  nodes that are a distance less or equal to
  transmission range due to omnidirectional
  antenna.

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Minimum Energy Node-disjoint paths

• Given an Energy Cost Graph G (V,E) with weights
  wij and source-destination pair S,D ? V , find a
  set of k node-disjoint S-D paths, P p1, p2, .
  . . , pk, such that E (P) is minimized.
• Energy Cost Equation
• E (P) T(S)
• T(S)
• (T(S) is transmission power of source node)

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Source Transmit Power Selection (STPS) algorithm
Energy cost graph
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Source Transmit Power Selection (STPS) algorithm

• Tradeoff between the current value of T(S) and
  the aggregate weight of the paths found by the
  minimum weight algorithm
• The worst case complexity of STPS algorithm
• O(kN3)
• The complexity of minimum weight node-disjoint
  paths algorithm is O(kN2).
• The algorithm iterates M-k1 times. (M N - 1)

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Minimum Energy Link-Disjoint Paths

• Given an Energy Cost Graph G (V,E) with weights
  wij and source-destination pair S,D ? V , find a
  set of k link-disjoint S-D paths,P p1, p2, . .
  . , pk, such that E (P) is minimized.
• Energy Cost Equation
• the pair of node-disjoint paths
  between node i and j belong to P

• 2 link disjoin paths
• common node
• ordered set of common node
• ex. C(P) c1, c2, , cz

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Optimal Common Node Decomposition (OCND) Algorithm
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Optimal Common Node Decomposition (OCND) Algorithm

• Overall complexity of O(kN5)
• Notion of Common Node decomposition not be easily
  extended to kgt2 disjoint path.
• When kgt2, a node may be common to a subset of the
  paths.

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Lower Complexity Heuristics

• Problems
• The complexity of the STPS and OCND is quite
  high.
• OCND algorithm only find 2 link disjoint paths
• Sub-optimal heuristic algorithm
• Heuristic 1 Naïve Dijkstra Agorithm
• Heuristic 2 Link-Disjoint Min-Weight (LD-MW)
  Algorithm
• Heuristic 3 WMA Enhanced link-disjoint Shortest
  Path (LD-ESP) Algorithm

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Results

• Node-disjoint Algorithm
• dijkatra algorithm lt ND-ESP lt LD-NW lt STPS
• Link-disjoint Algorithm
• dijkatra algorithm lt LD-MW lt LD-ESP lt OCND
• Energy cost comparison between optimal pairs of
  node and link-disjoint path
• Link disjoint paths are more energy efficient
• Cost of additional reliability
• Incremental energy of additional link-disjoint
  paths is decreasing.

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Distributed Implementation

• Distributed STPS
• Distributed OCND
• Dealing with topology changes

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Conclusion

• A polynomial time algorithm
• The minimum energy 2 link-disjoint paths problem
• The minimum energy k node-disjoint paths problem
• Heuristic algorithms
• link-disjoint paths more energy efficient than
  node-disjoint paths
• The incremental energy of additional
  link-disjoint paths is decreasing.