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Summary: JOURNAL OF ALGORJTHMS 7,567-583 (1986)
A Fast and Simple Randomized Parallel Algorithm
for the Maximal Independent Set Problem
NOGA ALON*
Department of Mathematics, Massachusetts Institute of Technoiogv, Cambridge,
Massachusetts 02139, and Department of Mathematics, Tel Aviv University,
Tel Aviv, Israel
LAsz~6BABAI
Department of Computer Science, University of Chicago, Chicago, Illinois 60637, and
Department ofAlgebra, Eiitviis University, Budapest, Hungary
AND
ALONITAI
Department of Computer Science, University of Chicago, Chicago, Illinois 60637, and
Department of Computer Science, Technion, Haifa, Israel
Received May 30,1985
A simple parallel randomized algorithm to find a maximal independent set in a
graph G = (V, E) on n vertices is presented. Its expected rmming time on a
concurrent-read concurrent-write PRAM with 0( 1E 1d,,) processors is O(log n),
where d,, denotes the maximum degree. On an exclusive-read exclusive-write
PRAM with 0( 1El) processors the algorithm runs in O(log2n). Previously, an
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