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 NC1.
|Title of host publication||Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992|
|Publisher||IEEE Computer Society|
|Number of pages||9|
|State||Published - 1992|
|Event||33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 - Pittsburgh, United States|
Duration: 24 Oct 1992 → 27 Oct 1992
|Name||Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS|
|Conference||33rd Annual Symposium on Foundations of Computer Science, FOCS 1992|
|Period||24/10/92 → 27/10/92|
Bibliographical notePublisher Copyright:
© 1992 IEEE.
ASJC Scopus subject areas
- Computer Science (all)