Coloring unstructured wireless multi-hop networks

We present a randomized coloring algorithm for the unstructured radio network model, a model comprising autonomous nodes, asynchronous wake-up, no collision detection and an unknown but geometric network topology. The current state-of-the-art coloring algorithm needs with high probability O(?log n) time and uses O() colors, where n and are the number of nodes in the network and the maximum degree, respectively; this algorithm requires knowledge of a linear bound on n and . We improve this result in three ways: Firstly, we improve the time complexity, instead of the logarithmic factor we just need a polylogarithmic additive term; more specifically, our time complexity is O(+log ?log n) given an estimate of n and , and O( + log2 n) without knowledge of . Secondly, our vertex coloring algorithm needs + 1 colors only. Thirdly, our algorithm manages to do a distance-d coloring with asymptotically optimal O() colors for a constant d. Categories and Subject Descriptors F.2.2 [Analysis of A...

• Type: Conference
• Year: 2009
• Where: PODC
• Authors: Johannes Schneider, Roger Wattenhofer
• Keywords: Parallel Computing, PODC 2009, Randomized Coloring Algorithm, State-of-the-art Coloring Algorithm, Vertex Coloring Algorithm