1. 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. 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. 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. 4 2P MAC Protocol 2 Synchronous operation –SynRx – Receiving phase –SynTx – Sending phase

5. 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. 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. 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. 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. 9 NP completeness of ZMCA Proof by reducing to an arbitrary instance of 3SAT I.Holyer - “The NP-Completeness of Edge- Colouring”

10. 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. 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. 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. 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. 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. 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. 16 Performance of Sum-Diffs and BFS –Sum-Diffs:4.78, BFS:4.47, (Match-DF only : 5.32)

17. 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. 18 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. 19 Local search heuristic –1.2 (Min-No-L-Search), 0.47 (L-Search), and 0.43 (OPT)

20. 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. 21 Thank you