Channel Allocation in 802'11based Mesh Networks

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Channel Allocation in 802.11-based Mesh Networks

• Infocom 06
• Bhaskaran Raman
• Dept. of CSE, IIT Kanpur, INDIA
• Presented by Jihyuk Choi
• 2006.10.31

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Contents

• 2P MAC Protocol
• Problem Statement
• Heuristics for Vizing
• Heuristics for Color Choice
• Heuristics for Edge Ordering.
• Local search heuristic
• Conclusion

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2P MAC Protocol

• Design and Evaluation of a new MAC Protocol for
  Long-Distance 802.11 Mesh Networks (Mobicom 05)
• TDMA style MAC protocol

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2P MAC Protocol

• Mesh network with
• Directional antenna
• Multiple adaptors
• Point to Point link
• Synchronous operation

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2P MAC Protocol

• Synchronous operation
• SynRx Receiving phase
• SynTx Sending phase

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Problem Statement

• Bipartition
• set of graph vertices decomposed into two
  disjoint sets such that no two graph vertices
  within the same set are adjacent.

Fixed Fraction f 1-f
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Problem Statement

• Links have various desired f value
• Skewed traffic of access network
• Use of Multi-channel
• There are 3 non-overlapping channel in 802.11
• split into subgraphs
• We can use several set of fractions for subgraphs
• Assigning the channel to each link
• Channel subgraph should be Bipartite

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Problem Statement

• BP-proper edge-coloring (NP-compelete)
• bipartite channel allocation
• BP-proper 3-edge-coloring is identical with
  proper 6-edge-coloring problem
• merge colors in pairs.
• We consider the class of network graphs that is
  6-edge-colorable
• ?5 where ? is maximum node degree
• By Vizings theorem, a graph with ?5 definitely
  has a proper 6-edge-coloring

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Problem Statement

• Selecting the pair among 6 colors.
• Assigning fraction for each subgraph to minimize
  AF-DF
• DF desired fraction
• AF achieved fraction
• ZMCA zero-mismatch channel allocation
• AF-DF0
• NP-complete

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Heuristics for MMCA

• MMCA minimum-mismatch channel allocation
  (NP-hard)
• step1 Vizing coloring (6 edge-coloring)
• color choice
• order in which edges are colored
• step2 color merging
• step3 Assignment of fraction to each subgraph

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Vizing Coloring

• Vizing coloring a method for edge coloring
• for each edge, choose a color that is absent at
  either end-point v1 and v2
• if no such common unused color is found, recolor
  v1 and v2 recursively
• we need heuristics because Vizing coloring is
  just for edge coloring (not for MMCA)

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Heuristics for Color Choice

• Greedy-Col heuristic
• while coloring an edge e
• for each color possible for e
• calculate mismatch cost of the subgraph has the
  same color with e
• choose the color which has minimum mismatch cost

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Heuristics for Color Choice

• Match-DF heuristic
• give preference to a color such that
• (a) color among the Greedy-Col
• (b) its counterpart color is already among the
  colors at v1 and/or v2
• (c) the edge(s) with the counterpart color at v1
  and/or v2 have the same DF as e
• if no colors satisfying (b) and (c) exist, the
  fall-back to (a)

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Performance of Greedy-Col and Match-DF

• 100 random topology with 50 nodes
• No-Heu10.58, Greedy-Col6.38, Match-DF5.32

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Heuristics for Edge Ordering

• Sum-Diffs heuristic
• Sum-Diffs(e) the sum of the difference between
  the DFs of edge e and each of its neighbors
• Try to color larger Sum-Diffs first.
• BFS heuristics
• ordering obtained by performing a BFS traversal

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Performance of Sum-Diffs and BFS

• 100 random topology with 50 nodes
• Sum-Diffs4.78, BFS4.47, (Match-DF only 5.32)

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Local search heuristic

• Comparison with optimal case for 20 node topology
• Avg. of 20 topologies 3.72 (No-Heu), 2.03
  (Greedy-Col), 1.55 (Match-DF), 1.31
  (Sum-DiffsMatch-DF), 1.40 (BFSMatch-DF)
• Optimal case 0.43
• Coloring matched for large part of the graph, but
  were different in small part.
• Local error correction heuristic is needed

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Local search heuristic

• Local search heuristic
• Subgraphs S1, S2, S3 are in decreasing order of
  mismatch cost.
• uncolor all edges of S1, and all the neighboring
  edges and recolor them exhaustively.
• the number of edges of subgraph is less than 20

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Local search heuristic

• 20 random topology with 20 nodes
• 1.2 (Min-No-L-Search), 0.47 (L-Search), and 0.43
  (OPT)

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Conclusion

• In this system, channel allocation can be (should
  be) pre-computed centrally and passed on to all
  nodes.
• Future works
• Angle of separation between two links.
• Calculation of effective DF for each link.
• Dynamic DF and dynamic Channel allocation
• Consider that some links are more important

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Comment

• Pros.
• Formation of problem Graph Theory
• Cons.
• TDMA style MAC
• Centralized
• Complexity
• ?5

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K-edge coloring

• A graph G is said to be k-edge colorable if its
  edges can be colored using up to k-colors such
  that no two edges with a vertex in common have
  the same color.