MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
The Power of Two Choices in Randomized Load Balancing
IEEE Transactions on Parallel and Distributed Systems
"Balls into Bins" - A Simple and Tight Analysis
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Random channel assignment in the plane
Random Structures & Algorithms
Distributed self-stabilizing placement of replicated resources in emerging networks
IEEE/ACM Transactions on Networking (TON)
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Fundamentals of wireless communication
Fundamentals of wireless communication
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Foundations and Trends® in Networking
Coloring spatial point processes with applications to peer discovery in large wireless networks
Proceedings of the ACM SIGMETRICS international conference on Measurement and modeling of computer systems
IEEE Communications Magazine
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In this paper, we study distributed channel assignment in wireless networks with applications to peer discovery in ad hoc wireless networks. We model channel assignment as a coloring problem for spatial point processes in which n nodes are located in a unit cube uniformly at random and each node is assigned one of K colors, where each color represents a channel. The objective is to maximize the spatial separation between nodes of the same color. In general, it is hard to derive the optimal coloring algorithm, and we therefore consider a natural online greedy coloring algorithm first proposed by Ko and Rubenstein in 2005. We prove two key results: 1) with just log n/log log n colors, the distance separation achieved by the greedy coloring algorithm asymptotically matches the optimal distance separation that can be achieved by an algorithm which is allowed to optimally place the nodes but is allowed to use only one color; and 2) when K = Ω(log n), the greedy coloring algorithm asymptotically achieves the best distance separation that can be achieved by an algorithm which is allowed to both optimally color and place nodes. The greedy coloring algorithm is also shown to dramatically outperform a simple random coloring algorithm. Moreover, the results continue to hold under node mobility.