Optimal Monitoring in Multi-Channel Multi-Radio Wireless Mesh Networks

Wireless mesh networks (WMN) are finding increasing usage in city-wide deployments for providing network connectivity. Mesh routers in WMNs typically use multiple wireless channels to enhance the spatial-reuse of frequency bands, often with multiple radios per node. Due to the cooperative nature of WMNs, they are susceptible to many attacks that cannot be defeated by using traditional cryptographic mechanisms of authentication or encryption alone. A solution approach commonly used for defending against such attacks is behavior-based detection in which some nodes overhear communication in their neighborhood to determine if the behavior by a neighbor is legitimate. It, has been proposed to use specialized monitoring nodes deployed strategically throughout the network for performing such detection. The problem that arises is where to deploy these monitoring nodes, how to minimize their number, and which channels to tune their radios to, such that the maximum part of the network can be covered. This problem has been solved for single channel networks by a greedy approximation algorithm since the exact solution is NP-hard. The greedy algorithm achieves the best performance, in terms of the worst case, possible among all polynomial-time algorithms provided that P not equal NP. In this paper, we solve the problem for multi-channel multi-radio WMNs. The intuitive extension of the greedy algorithm destroys the property of best performance. Instead, we formulate the problem as an integer linear program, solve its linear program relaxation, and then use two rounding techniques that we develop by adapting existing rounding schemes. We thereby present two approximation algorithms. The first, computationally-light algorithm, called probabilistic rounding algorithm gives an expected best performance in the worst case. The second, called deterministic rounding algorithm achieves the best worst-case performance in a deterministic manner. To evaluate how the three algorithms perform in practice, we simulate them in random networks and scale-free networks.