Proceedings., 33rd Annual Symposium on Foundations of Computer Science (1992)
Pittsburgh, PA, USA
Oct. 24, 1992 to Oct. 27, 1992
N. Alon , Dept. of Math., Raymond&Beverly Sackler Faculty of Exact Sciences, Tel Aviv Univ., Israel
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/.
partition, parallelism, regularity lemma, computational difficulty, regular partition, input graph
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.