A new parallel algorithm for the maximal independent set problem

1987 ◽  
Author(s):  
Mark Goldberg ◽  
Thomas Spencer
Keyword(s):  
Parallel Algorithm ◽  
Independent Set ◽  
Maximal Independent Set ◽  
Independent Set Problem

A RANDOMIZED BSP/CGM ALGORITHM FOR THE MAXIMAL INDEPENDENT SET PROBLEM

1999 ◽  
Vol 09 (03) ◽  
pp. 411-422 ◽  
Author(s):  
AFONSO FERREIRA ◽  
NICOLAS SCHABANEL
Keyword(s):  
Parallel Algorithm ◽  
High Probability ◽  
Independent Set ◽  
Computation Time ◽  
Log P ◽  
Maximal Independent Set ◽  
Search Problem ◽  
Constant Number ◽  
Independent Set Problem

This paper presents a randomized parallel algorithm for the Maximal Independent Set problem. Our algorithm uses a BSPlike computer with p processors and requires that [Formula: see text] 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 [Formula: see text]. 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 BSPCGM algorithm to the p-quantiles search problem, which runs in [Formula: see text] time and a constant number of communication rounds, and could be of interest in its own right, as shown in the text.

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