Channel Assignment in Wireless Networks: Graph Coloring Presented by: Andrew Chickadel – Villanova University

What is Channel Assignment? Selecting radio frequencies for: Enhanced security Reducing interference Keeping in mind: Radio frequency (RF) spectrum Network topologies Security: generally prevents others from accidentally receiving packets which might contain sensitive information Reducing interference relies on assigning channels that do not or only slightly conflict with each other. Graph coloring will play a huge role in this task RF spectrum: limited number of channels available…increasing the number of channels increases chances for interference to occur Topologies: (the structure of the network) can be changed if channels are assigned dynamically…also want to avoid overly complex topologies

What is Graph Coloring? Generally defined as: Edge Coloring NP-complete for determining class Vertex Coloring NP-hard for general graphs Channels represented as “colors” Edge: class 1 contains bipartite graphs, class two contains all others. NP-complete to determine which class FOR EDGE COLORING, NO VERTEX CAN HAVE MORE THAN ONE OUTGOING EDGE OF A PARTICULAR COLOR ************NP-complete contains NP-hard, so NP-complete is the hardest of all NP problems Vertex: NO VERTEX CAN HAVE THE SAME COLOR AS AN ADJACENT (connected) VERTEX

Why Graph Coloring? Practicality Relevance Reliability Practical – rather than develop super-advanced radio frequency technology or invest money in fixing the problem at the most Relevance – preventing vertices from connecting with conflicting vertices is the quintessential task in reducing network interference Reliability – graph coloring algorithms are proven mathematical processes and addressing the issue of interference at a low level hinders complications in general, high-level implementation

Interference

Interference Solved by Edge Coloring How many colors do we need? It depends on the number of outgoing edges!

Interference Solved by Vertex Coloring How many colors do we need? It depends on the overall complexity and connectivity of the graph!

Coloring Implementations Weighted coloring Channel re-use algorithms Dynamic channel assignment RF spectrum boundary algorithms Multi-step algorithms Weighted: assigning weights to graph edges based on, say bandwidth demand, in order to properly allocate the finite amount of channels to transmitters Re-use: ex…computes a minimum distance in order to ensure vertices are far enough away to re-use a particular channel Dynamic: re-assigning channels based on the amount of interference experienced at each transmitter RF bounds: compute bounds for the number of radio frequencies to use in a given network Multi-step: using more than one assignment methods in one algorithm

Dynamic Assignment Almeroth et al.1 Shortcomings Future improvements Dramatic topology changes Security across the “default channel” Future improvements Dense settings 1 K.N. Ramachandran, E. M. Belding, K.C. Almeroth, M.M. Buddhikot, “Interference-Aware Channel Assignment in Multi-Radio Wireless Mesh Networks,” Apr. 2006; http://www.cs.ucsb.edu/~ebelding/txt/infocom06.pdf Almeroth et al.: Based on an interference value, the graph reassigns a channel to a particular vertex and changes the graph and connections to reduce interference across the new channel. However, the network topology is subject to massive alteration. They suggest the use of a default channel by which all nodes can communicate in a situation where connections are dropped until connection is restored. The algorithm uses a breadth-first search of the connectivity graph to award priority values and thus assigns channels based on priority. BFS traverses the graph beginning at the most dense nodes and eventually fanning out to nodes with the fewest connections RESULTS: ****SHOWED VERY LITTLE IMPROVEMENT IN DENSE ENVIRONMENTS****

A Multi-step Algorithm Hminmax: Arbaugh et al.2 Shortcomings “Greedy” step Algorithmic complexity not improved, only numerical results Future improvements Overlapping 802.11b/g interference graphs 802.11b/g in same coverage area 2 A. Mishra, S. Banerjee, W. Arbaugh, “Weighted Coloring Based Channel Assignment for WLANs,” ACM SIGMOBILE Mobile Computing and Communications Review, July 2005, vol. 9, no. 3, pp. 19-31. Arbaugh et al.: A distributed algorithm which executes in two steps: the first step, the initialization where nodes are all assigned channels to broadcast over. The second step involves greedily determining which channel would cause and receive the least interference as a result of channel reassignment and reassigns the channel accordingly…and so on all throughout the network. RESULTS: 40% OVERALL DROP IN INTERFERENCE ****DID NOT TEST IN B/G ENVIRONMENT****

Looking Ahead Improvement despite NP-hard and NP-complete Rapid growth of Wi-fi and effects on the RF spectrum Security must be maintained GROWTH OF WI-FI: As networks become more dense, interference will become more of an issue. Algorithms must be presented that deal with dense environments as well as algorithms that work well in new drafts of Wi-fi technology (draft N and beyond). More and more expansive networks will require more of the narrow RF band. SECURITY: More interference means security measures must remain updated and effective