Parallel Architectures, Algorithms, and Networks, International Symposium on (1999)

Fremantle, Australia

June 23, 1999 to June 25, 1999

ISSN: 1087-4089

ISBN: 0-7695-0231-8

pp: 284

Afonso Ferreira , CNRS - I3S - INRIA

Nicolas Schabanel , LIP-ENS

ABSTRACT

This paper presents a randomized parallel algorithm for the Maximal Independent Set problem. Our algorithm uses a BSP-like computer with p processors and requires (n+m)/p larger or equal to p for a graph with n vertices and m edges. Under this scalability assumption, and after a preprocessing phase, it computes a maximal independent set after O(log p) communication rounds, with high probability, each round requiring linear computation time O((n+m)/p). The preprocessing phase is deterministic and important in order to ensure that degree computations can be implemented efficiently. For this, we give an optimal parallel BSP/CGM algorithm to the p-quantiles search problem, which runs in O(m log p/p) time and a constant number of communication rounds, and could be of interest in its own right, as shown in the full text.

INDEX TERMS

Parallel Algorithms, Maximal Independent Set, Randomized Algorithms, Graph Algorithms, Coarse-Grained Models, BSP, CGM, p-quantiles Search, Sorting

CITATION

N. Schabanel and A. Ferreira, "A Randomized BSP/CGM Algorithm for the Maximal Independent Set Problem,"

*Parallel Architectures, Algorithms, and Networks, International Symposium on(ISPAN)*, Fremantle, Australia, 1999, pp. 284.

doi:10.1109/ISPAN.1999.778953

CITATIONS