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Channel Allocation in 802.11-based Mesh Networks

Channel Allocation in 802.11-based Mesh Networks. Infocom ‘ 06 Bhaskaran Raman Dept. of CSE, IIT Kanpur, INDIA Presenter Janghwan Lee 2006.9.28. Contents. 2P MAC Protocol 1 Problem Statement NP completeness of ZMCA Heuristics for Vizing Heuristics for Color Choice

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Channel Allocation in 802.11-based Mesh Networks

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  1. Channel Allocation in 802.11-based Mesh Networks Infocom ‘06 Bhaskaran Raman Dept. of CSE, IIT Kanpur, INDIA Presenter Janghwan Lee 2006.9.28

  2. Contents • 2P MAC Protocol 1 • Problem Statement • NP completeness of ZMCA • Heuristics for Vizing • Heuristics for Color Choice • Heuristics for Edge Ordering. • Local search heuristic • Discussion

  3. 2P MAC Protocol 1 • “Design and Evaluation of a new MAC Protocol for Long-Distance 802.11 Mesh Networks” (Mobicom 05) • Mesh network with… • Directional antenna • Multiple adaptors • Point to Point link • Synchronous operation

  4. 2P MAC Protocol 2 • Synchronous operation • SynRx – Receiving phase • SynTx – Sending phase

  5. 2P MAC Protocol 3 • 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

  6. 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

  7. Problem Statement 2 • BP-proper edge-colouring (NP-compelete) • bipartite channel allocation • BP-proper 3-edge-colouring is identical with proper 6-edge-colouring problem • merge colours in pairs. • We consider the class of network graphs that is 6-edge-colourable • Δ≤5 where Δ is maximum node degree

  8. Problem Statement 3 • Selecting the pair among 6 colours. • Assigning fraction for each subgraph to minimize |AF-DF| • DF: desired fraction • AF: achieved fraction • ZMCA : zero-mismatch channel allocation • |AF-DF|=0

  9. NP completeness of ZMCA • Proof by reducing to an arbitrary instance of 3SAT • I.Holyer - “The NP-Completeness of Edge-Colouring”

  10. Heuristics for MMCA • MMCA: minimum-mismatch channel allocation • step1 : Vizing colouring (6 edge-colouring) • Colour choice • Order in which edges are coloured • step2 : Colour merging • Constant coefficient • step3 : Assignment of fraction to each subgraph • straight forward

  11. Vizing Coloring • Vizing Colouring – a method for edge coloring • for each edge, choose a colour that is absent at either end-point v1 and v2 • if no such common unused colour is found, recolour 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 colouring an edge e • for each colour possible for e • calculate mismatch cost of the subgraph has the same colour with e • choose the colour 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 colour at v1 and/or v2 have the same DF as e • if no colours 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-Hew:10.58, Greedy-Col:6.38, Match-DF:5.32

  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 • Sum-Diffs:4.78, BFS:4.47, (Match-DF only : 5.32)

  17. Local search heuristic • Comparison with optimal case for 20 node topology • 3.72 (No-Heu), 2.03 (Greedy-Col), 1.55 (Match-DF), 1.31 (Sum-Diffs::Match-DF), 1.40 (BFS::Match-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. • Recalculate S1, S2, S3… iteratively • the number of edges of subgraph is less than 20

  19. Local search heuristic • 1.2 (Min-No-L-Search), 0.47 (L-Search), and 0.43 (OPT)

  20. Discussion • In this system, channel allocation can be (should be) pre-computed centrally and passed on to all nodes. • Angle of separation between two links. • Calculation of effective DF for each link.

  21. Thank you

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