1. Optimization Models for Fixed Channel Assignment in Wireless Mesh Networks with Multiple Radios Arindam K. Das, Sumit Roy, SECON 2005 2006.11.2 Kim Young Hoon yhoon@cnlab.kaist.ac.kr

2. Introduction Channel assignment problem in Multi-channel Multi-hop Environment Link model, not node model Integer Linear Programming –In mathematics, linear programming (LP) problems are optimization problems in which the objective function and the constraints are all linear. If the unknown variables are all required to be integers, then the problem is called an integer programming (IP) or integer linear programming (ILP) problem.

3. Object and Challenge Maximization of the number of possible simultaneous transmissions in the network Objective Function –Fixed channel assignment with multiple radios Challenge –Avoid potential link interference

4. Try it Difference between edge coloring and this problem

5. ILP constraints 1.Every link has one channel assignment 2.If a channel is assigned to a neighbor of a node, that node should have a link with that channel 3.The number of distinct channels assigned to any node is less than or equal to the number of radios at each node 4.Within interference range, two links assigned same channel cannot be in optimal solution together 5.Number of links in optimal solution for one node is less than or equal to the number of channels assigned to that node 6.Maximum number of links which can be simultaneously activated in a potentially interferencing clique of edges is the number of channels

6. ILP Models ILP Model ‘A’ – each link can be assigned to one of F channels ILP Model ‘B’ – each link means specific channel

7. ILP Model ‘A’ Variables –Y nf : whether node n has channel f as its link –C ef : whether channel f assign to link e –X e : whether link e is in optimal solution –F: set of channels –rows(n): link k is incident to n –LIM: link interference matrix –IC: interference clique 6 4 3 2 1 5

8. ILP Model ‘B’ Variables –Y nf : whether node n has channel f as its link –C ef : whether channel f assign to link e –X ef : whether link (e,f) is in optimal solution –F: set of channels –rows(n): link k is incident to n –LIM: link interference matrix –IC: interference clique

9. Simulation Result (A) Solver times and optimal ILP costs (B) Comparison of solver times for models ‘A’ and ‘B’ (A) (B)

10. Conclusion Authors have presented two ILP formulations for the fixed channel assignment problem in multi- radio meshes with the goal of maximizing the number of simultaneous transmissions in the network