Network decomposition and locality in distributed computation

Abstract

The authors introduce a concept of network decomposition, a partitioning of an arbitrary graph into small-diameter connected components, such that the graph created by contracting each component into a single node has low chromatic number. They present an efficient distributed algorithm for constructing such a decomposition and demonstrate its use for design of efficient distributed algorithms. The method yields new deterministic distributed algorithms for finding a maximal independent set in an arbitrary graph and for ( Delta +1)-coloring of graphs with maximum degree Delta . These algorithms run in O(n/sup epsilon /) time for epsilon =O((log log n/log n)/sup 1/2/), whereas the best previously known deterministic algorithms required Omega (n) time. The techniques can also be used to remove randomness from the previously known most distributed breadth-first search algorithm.