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Channel Allocation in 802.11based Mesh Networks

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By Vizing's theorem, a graph with ?5 definitely has a proper 6-edge-coloring. 9 ... Coloring matched for large part of the graph, but were different in small part. ... – PowerPoint PPT presentation

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Title: Channel Allocation in 802.11based Mesh Networks


1
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

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

3
2P MAC Protocol
  • Design and Evaluation of a new MAC Protocol for
    Long-Distance 802.11 Mesh Networks (Mobicom 05)
  • TDMA style MAC protocol

4
2P MAC Protocol
  • Mesh network with
  • Directional antenna
  • Multiple adaptors
  • Point to Point link
  • Synchronous operation

5
2P MAC Protocol
  • Synchronous operation
  • SynRx Receiving phase
  • SynTx Sending phase

6
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
7
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

8
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

9
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

10
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

11
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)

12
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

13
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)

14
Performance of Greedy-Col and Match-DF
  • 100 random topology with 50 nodes
  • No-Heu10.58, Greedy-Col6.38, Match-DF5.32

15
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

16
Performance of Sum-Diffs and BFS
  • 100 random topology with 50 nodes
  • Sum-Diffs4.78, BFS4.47, (Match-DF only 5.32)

17
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

18
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

19
Local search heuristic
  • 20 random topology with 20 nodes
  • 1.2 (Min-No-L-Search), 0.47 (L-Search), and 0.43
    (OPT)

20
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

21
Comment
  • Pros.
  • Formation of problem Graph Theory
  • Cons.
  • TDMA style MAC
  • Centralized
  • Complexity
  • ?5

22
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.
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