Routing in Trees

Given an undirected graph with positive edge weights, define Nq(v) for each node v to be the set of q nodes closest to v (including v itself and breaking ties by node ID). It is shown that the nodes of any tree can be colored with one color per node drawn from a set of q colors, so that, for each node v, each color appears exactly once in Nq(v) (but for arbitrary graphs, verifying whether they can be similarly colored for constant q is NP-Complete). As an application of the first result, we present a generalized tradeoff scheme that, for any fixed constant k and any 2 ≤ b ≤ O(n1/k ), uses space O(n1/k logb n log n), headers of length O(logb n log n), makes intermediate routing decisions in O(log b) time, and achieves stretch 2k

• Type: Conference
• Year: 2001
• Where: ICALP
• Authors: Pierre Fraigniaud, Cyril Gavoille
• Keywords: ICALP 2001, Node, Node Id, Positive Edge Weights, Programming Languages