An Algorithmic Version of the Hypergraph Regularity Method
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Hypergraph regularity and quasi-randomness
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Szemerédi's regularity lemma and its applications to pairwise clustering and segmentation
EMMCVPR'07 Proceedings of the 6th international conference on Energy minimization methods in computer vision and pattern recognition
Can a graph have distinct regular partitions?
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
| Hi-index | 0.00 |
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/.