Multicast%20Routing%20with%20Minimum%20Energy%20Cost%20in%20Ad%20hoc%20Wireless%20Networks

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Multicast Routing with Minimum Energy Cost in Ad
hoc Wireless Networks

• Xiaohua Jia, Deying Li and Frankie Hung
• Dept of Computer Science,
• City Univ of Hong Kong

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Energy-efficiency in ad hoc networks

• Power function
• p(u,v) da(u,v), 2 a 4
• Two special features of radio transmission
• Broadcast in nature.
• p(u,w) p(w,v) lt p(u,v),
• relaying messages by a third node may result in
  a smaller energy cost.

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Multicast Routing with Min Energy Cost

• Problem Given a directed network graph G(V,A),
  and a multicast request (s, D), each node v has
  a given transmission power p(v), find a multicast
  tree T rooted at s and covering all nodes in D,
  such that
• where NL(T) is the set of non-leaf nodes of T.

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Related Work
BIP / MIP (Multicast Incremental Power) BIP is
based on Prims MST algorithm. Starting from s,
each time a node with least incremental power is
added to the tree, until all nodes are in the
tree. MIP tree is obtained by pruning the BIP
tree. J.E. Wieselthier, G. D. Nguyen, and A.
Ephremides, On the Construction of
Energy-Efficient Broadcast and Multicast Trees in
Wireless Networks, IEEE Infocom00.
s
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Related Wrok (Contd)

• Deying Li, Xiaohua Jia and Hai Liu, Energy
  Efficient Broadcast Routing in Ad Hoc Wireless
  Networks, IEEE Trans. On Mobile Computing ,
  vol.3, no.2, 2004.
• An approximation algorithm based on node-weighted
  Steiner tree method was proposed and the
  approximation ratio is 2ln(n-1)1.

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Theoretical Results
The energy efficient multicast routing problem is
NP-Hard and there is NO constant approximation
ratio.
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Heuristic A. Transforming the problem to the
Steiner tree problem

• The multicast routing problem is transformed to
  finding a directed tree T in G that covers all
  nodes in D and the total weights of T (edge
  weights) is minimized.

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Heuristic B. Node-join-Tree method

• Vi set of outgoing neighbors of node i
• C s // C covered set
• U D - Vs // U uncovered set
• X Vs // X candidate set for covering nodes
• While (U ?? ) do
• choose vi ? (X C) with max(VinU/p(i))
• C C? vi U (U Vi) X X? Vi

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Heuristic C. Tree-join-Tree method

• The basic idea is
• Initially, each node in D is a subtree.
• Find a node v ? V that uses the least amount of
  energy to link the roots of at least two subtrees
  and merge them into a bigger one (v becomes the
  root of the new subtree).
• Repeat (2) until all subtrees form into a single
  tree rooted at s.

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Heuristic C. Tree-join-Tree method (contd)

• Orphan a subtree whose root is not s.
• O the set of orphans.
• min-quotient-cost(v) MinS ? O
  TreeCost(v,S)/S for S ? O.
• O i i? D)
• While (O ?? ) do
• choose v ? V with Min min-quotient-cost(v)
• link v to the roots of the orphans by shortest
  paths

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Simulation Results
N50, R0.2
Energy cost vs. multicast group size
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Simulation Results (Contd)
M10, R0.2
Energy cost vs. network size
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Simulation Results (Contd)
M10, R
Energy cost vs. network size
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Simulation Results (Contd)
M10, N50
Energy cost vs. transmission range
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Conclusions

• Investigated energy efficient multicast routing
  problem.
• Three heuristic methods, Steiner tree based,
  node-join-tree, and tree-join-tree, were
  proposed.
• The node-join-tree method can be extended to a
  distributed version. It uses only the neighbour
  information to construct the multicast tree.
• Simulation results suggested the simple
  node-join-tree method performs the best among the
  other methods.