Efficient Parallel and External Matching

TL;DR

This paper presents a simple, efficient parallel and external memory algorithm for graph matching that runs in logarithmic phases, adapts well across various computational models, and demonstrates high speed and quality in experiments.

Contribution

It introduces the first O(log^2 n) time, linear work algorithm for graph matching on CREW PRAM and adapts it to multiple computational models.

Findings

Algorithm runs in logarithmic phases with linear work.

Experimental results show high speed and efficiency.

Algorithm achieves good solution quality.

Abstract

We show that a simple algorithm for computing a matching on a graph runs in a logarithmic number of phases incurring work linear in the input size. The algorithm can be adapted to provide efficient algorithms in several models of computation, such as PRAM, External Memory, MapReduce and distributed memory models. Our CREW PRAM algorithm is the first O(log^2 n) time, linear work algorithm. Our experimental results indicate the algorithm's high speed and efficiency combined with good solution quality.