• Channel Assignment in Wireless Networks:

Graph ColoringPresented 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

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”

Why Graph Coloring?

• Practicality

• Relevance

• Reliability

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

Dynamic Assignment• Almeroth et al.1

• Shortcomings– 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

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.

Looking Ahead

• Improvement despite NP-hard and NP-complete

• Rapid growth of Wi-fi and effects on the RF spectrum

• Security must be maintained