An Algorithmic Version of the Blow-Up Lemma

János Komlós, Gabor N. Sarkozy, E. Szemerédi

Research output: Contribution to journalArticle

59 Citations (Scopus)

Abstract

Recently we developed a new method in graph theory based on the regularity lemma. The method is applied to find certain spanning subgraphs in dense graphs. The other main general tool of the method, besides the regularity lemma, is the so-called blow-up lemma (Komlós, Sárközy, and Szemerédi [Combinatorica, 17, 109-123 (1997)]. This lemma helps to find bounded degree spanning subgraphs in ε-regular graphs. Our original proof of the lemma is not algorithmic, it applies probabilistic methods. In this paper we provide an algorithmic version of the blow-up lemma. The desired subgraph, for an n-vertex graph, can be found in time O(nM(n)), where M(n) = O(n2.376) is the time needed to multiply two n by n matrices with 0, 1 entires over the integers. We show that the algorithm can be parallelized and implemented in NC5.

Original languageEnglish
Pages (from-to)297-312
Number of pages16
JournalRandom Structures and Algorithms
Volume12
Issue number3
Publication statusPublished - May 1998

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Graph theory
Blow-up
Lemma
Regularity Lemma
Spanning Subgraph
Probabilistic Methods
Graph in graph theory
Regular Graph
Subgraph
Multiplication
Entire
Integer
Vertex of a graph

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Mathematics(all)
  • Applied Mathematics

Cite this

An Algorithmic Version of the Blow-Up Lemma. / Komlós, János; Sarkozy, Gabor N.; Szemerédi, E.

In: Random Structures and Algorithms, Vol. 12, No. 3, 05.1998, p. 297-312.

Research output: Contribution to journalArticle

Komlós, J, Sarkozy, GN & Szemerédi, E 1998, 'An Algorithmic Version of the Blow-Up Lemma', Random Structures and Algorithms, vol. 12, no. 3, pp. 297-312.
Komlós, János ; Sarkozy, Gabor N. ; Szemerédi, E. / An Algorithmic Version of the Blow-Up Lemma. In: Random Structures and Algorithms. 1998 ; Vol. 12, No. 3. pp. 297-312.
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