Best of Two Local Models: Centralized Local and Distributed Local Algorithms.

We consider two models of computation: centralized local algorithms and local distributed algorithms. Algorithms in one model are adapted to the other model to obtain improved algorithms.Distributed vertex coloring is employed to design improved centralized local algorithms for: maximal independent set, maximal matching, and an approximation scheme for maximum (weighted) matching over bounded degree graphs. The improvement is threefold: the algorithms are deterministic, stateless, and the number of probes grows polynomially in log⁎⁡n, where n is the number of vertices of the input graph.The recursive centralized local improvement technique by Nguyen and Onak (FOCS 2008) is employed to obtain a distributed approximation scheme for maximum (weighted) matching.