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

We consider two models of computation: local centralized 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 local centralized algorithms for: maximal independent set, maximal matching, and an approximation scheme for maximum matching over bounded degree graphs. The improvement is threefold: the algorithms are deterministic, stateless, and the number of probes is poly(log n). The recursive local centralized improvement technique by Nguyen and Onak [NO08] is employed to obtain an improved distributed approximation scheme for maximum matching. The number of rounds of the distributed algorithm is O(log n) for bounded degree graphs.