Proceedings., 33rd Annual Symposium on Foundations of Computer Science (1992)

Pittsburgh, PA, USA

Oct. 24, 1992 to Oct. 27, 1992

ISBN: 0-8186-2900-2

pp: 473-481

N. Alon , Dept. of Math., Raymond&Beverly Sackler Faculty of Exact Sciences, Tel Aviv Univ., Israel

ABSTRACT

The regularity lemma of Szemeredi (1978) is a result that asserts that every graph can be partitioned in a certain regular way. This result has numerous applications, but its known proof is not algorithmic. The authors first demonstrate the computational difficulty of finding a regular partition; they show that deciding if a given partition of an input graph satisfies the properties guaranteed by the lemma is co-NP-complete. However, they also prove that despite this difficulty the lemma can be made constructive; they show how to obtain, for any input graph, a partition with the properties guaranteed by the lemma, efficiently. The desired partition, for an n-vertex graph, can be found in time O(M(n)), where M(n)=O(n/sup 2.376/) is the time needed to multiply two n by n matrices with 0,1-entries over the integers. The algorithm can be parallelized and implemented in NC/sup 1/.

INDEX TERMS

partition, parallelism, regularity lemma, computational difficulty, regular partition, input graph

CITATION

N. Alon, "The algorithmic aspects of the regularity lemma,"

*Proceedings., 33rd Annual Symposium on Foundations of Computer Science(FOCS)*, Pittsburgh, PA, USA, 1992, pp. 473-481.

doi:10.1109/SFCS.1992.267804

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