A simple algorithm for constructing Szemerédi's Regularity Partition (1999)
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| Venue: | Electr. J. Comb |
| Citations: | 10 - 0 self |
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@ARTICLE{Frieze99asimple,
author = {Alan Frieze and Ravi Kannan},
title = {A simple algorithm for constructing Szemerédi's Regularity Partition},
journal = {Electr. J. Comb},
year = {1999},
volume = {6},
pages = {pp. (electronic).}
}
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Abstract
We give a simple constructive version of Szemer'edi's Regularity Lemma, based on the computation of singular values of matrices. Mathematical Reviews Subject Numbers: 05C85, 68R10. 1 Introduction "Szemer'edi's Regularity Lemma [9] is one of the most powerful tools of (extremal) graph theory". One can only agree with that opening sentence of the Supported in part by NSF grant CCR-9530974. y Supported in part by NSF grant CCR-9528973. the electronic journal of combinatorics 6 (1999), #R17 2 paper by Koml'os and Simonovits [6]. It has many, many applications and we refer the reader to this excellent survey. The Regularity lemma is often used to prove the existence of certain objects and if in addition one wants to construct them, then one needs a constructive version of the lemma. This was provided by Alon, Duke, Lefmann, Rodl and Yuster [1]. Subsequently, Frieze and Kannan [3, 4] gave a different version and extended it to deal with hypergraphs, (see also Czygrinow and Rodl [2])....
Citations
| 259 | Probabilistic construction of deterministic algorithms: approximating packing integer programs - RAGHAVAN - 1988 |
| 172 | Szemerédi’s regularity lemma and its applications in graph theory - Komlós, Simonovits - 1993 |
| 112 | Regular Partitions of Graphs - Szemerédi - 1976 |
| 96 | Quick approximation to matrices and applications - Frieze, Kannan - 1999 |
| 70 | The regularity lemma and approximation schemes for dense problems - Frieze, Kannan - 1996 |
| 53 | Ten lectures on the probabilistic method - Spencer - 1987 |
| 12 | An algorithmic regularity lemma for hypergraphs - Czygrinow, Rödl |
| 3 | V.Rodl and R.Yuster, The algorithmic aspects of the Regularity - Alon, Lefmann - 1994 |
