TY - JOUR

T1 - A fast and simple randomized parallel algorithm for the maximal independent set problem

AU - Alon, Noga

AU - Babai, László

AU - Itai, Alon

N1 - Funding Information:
*Research supported in part by the Weizmamt Fellowship for Scientific Research and by NSF Grant 8406100.

PY - 1986/12

Y1 - 1986/12

N2 - A simple parallel randomized algorithm to find a maximal independent set in a graph G = (V, E) on n vertices is presented. Its expected running time on a concurrent-read concurrent-write PRAM with O(|E|dmax) processors is O(log n), where dmax denotes the maximum degree. On an exclusive-read exclusive-write PRAM with O(|E|) processors the algorithm runs in O(log2n). Previously, an O(log4n) deterministic algorithm was given by Karp and Wigderson for the EREW-PRAM model. This was recently (independently of our work) improved to O(log2n) by M. Luby. In both cases randomized algorithms depending on pairwise independent choices were turned into deterministic algorithms. We comment on how randomized combinatorial algorithms whose analysis only depends on d-wise rather than fully independent random choices (for some constant d) can be converted into deterministic algorithms. We apply a technique due to A. Joffe (1974) and obtain deterministic construction in fast parallel time of various combinatorial objects whose existence follows from probabilistic arguments.

AB - A simple parallel randomized algorithm to find a maximal independent set in a graph G = (V, E) on n vertices is presented. Its expected running time on a concurrent-read concurrent-write PRAM with O(|E|dmax) processors is O(log n), where dmax denotes the maximum degree. On an exclusive-read exclusive-write PRAM with O(|E|) processors the algorithm runs in O(log2n). Previously, an O(log4n) deterministic algorithm was given by Karp and Wigderson for the EREW-PRAM model. This was recently (independently of our work) improved to O(log2n) by M. Luby. In both cases randomized algorithms depending on pairwise independent choices were turned into deterministic algorithms. We comment on how randomized combinatorial algorithms whose analysis only depends on d-wise rather than fully independent random choices (for some constant d) can be converted into deterministic algorithms. We apply a technique due to A. Joffe (1974) and obtain deterministic construction in fast parallel time of various combinatorial objects whose existence follows from probabilistic arguments.

UR - http://www.scopus.com/inward/record.url?scp=0001011699&partnerID=8YFLogxK

U2 - 10.1016/0196-6774(86)90019-2

DO - 10.1016/0196-6774(86)90019-2

M3 - מאמר

AN - SCOPUS:0001011699

VL - 7

SP - 567

EP - 583

JO - Journal of Algorithms

JF - Journal of Algorithms

SN - 0196-6774

IS - 4

ER -