Distributed Node Coloring in the SINR Model

• Published in: 2010 IEEE 30th International Conference on Distributed Computing Systems pp. 708 - 717
• Main Authors: Derbel, B, Talbi, E
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.06.2010
• Subjects: Access protocols; Color; Coloring; Distributed Algorithm; Distributed algorithms; Distributed computing; Interference constraints; Media Access Protocol; Radio communication; Radio network; Signal to noise ratio; SINR Model; TDMA; Time Complexity; Wireless sensor networks
• ISBN: 142447261X; 9781424472611
• ISSN: 1063-6927
• DOI: 10.1109/ICDCS.2010.35

Given a palette P of at most V colors, and a parameter d, a (d, V)-coloring of a graph is an assignment of a color from the palette P to every node in the graph such that any two nodes at distance at most d have different colors. We prove that for every n-node unit disk graph with maximum degree Δ, there exists a distributed algorithm computing a (1,O(Δ))-coloring under the SINR (Signal-to-Interferenceplus-Noise Ratio) physical model in at most O(Δ log n) time slots, which is optimal up to a logarithmic factor. Our result is based on revisiting a previous coloring algorithm, due to T. Moscibroda and R. Wattenhofer, described in the so called graph-based model. We also prove that, for a well defined constant d, a (d, O(Δ))-coloring allows us to schedule an interference free TDMA-like MAC protocol under the physical SINR constraints. As a corollary, any uniform interferencefree message passing algorithm with running time r can be simulated in the SINR model in O(Δ(log n+τ)) time slots. The latter generic result provides new insights into the distributed scheduling of radio network tasks under the harsh SINR constraints.