Quasi-randomness and algorithmic regularity for graphs with general degree distributions

Noga Alon; Amin Coja-Oghlan; Hiêp Hàn; Mihyun Kang; Vojtěch Rödl; Mathias Schacht

doi:10.1007/978-3-540-73420-8_68

Quasi-randomness and algorithmic regularity for graphs with general degree distributions

Noga Alon^*
, Amin Coja-Oghlan
, Hiêp Hàn
, Mihyun Kang
, Vojtěch Rödl
, Mathias Schacht

^*Corresponding author for this work

School of Computer Science and AI

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

We deal with two very related subjects: quasi-randomness and regular partitions. The purpose of the concept of quasi-randomness is to measure how much a given graph "resembles" a random one. Moreover, a regular partition approximates a given graph by a bounded number of quasi-random graphs. Regarding quasi-randomness, we present a new spectral characterization of low discrepancy, which extends to sparse graphs. Concerning regular partitions, we present a novel concept of regularity that takes into account the graph's degree distribution, and show that if G = (V, E) satisfies a certain boundedness condition, then G admits a regular partition. In addition, building on the work of Alon and Naor [4], we provide an algorithm that computes a regular partition of a given (possibly sparse) graph G in polynomial time.

Original language	English
Title of host publication	Automata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings
Publisher	Springer Verlag
Pages	789-800
Number of pages	12
ISBN (Print)	3540734198, 9783540734192
DOIs	https://doi.org/10.1007/978-3-540-73420-8_68
State	Published - 2007
Event	34th International Colloquium on Automata, Languages and Programming, ICALP 2007 - Wroclaw, Poland Duration: 9 Jul 2007 → 13 Jul 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4596 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	34th International Colloquium on Automata, Languages and Programming, ICALP 2007
Country/Territory	Poland
City	Wroclaw
Period	9/07/07 → 13/07/07

Funding

Funders	Funder number
Directorate for Mathematical and Physical Sciences	0300529, 0800070

Keywords

Grothendieck's inequality
Laplacian eigenvalues
Quasi-random graphs
Regularity lemma
Sparse graphs

Access to Document

10.1007/978-3-540-73420-8_68

Cite this

Alon, N., Coja-Oghlan, A., Hàn, H., Kang, M., Rödl, V., & Schacht, M. (2007). Quasi-randomness and algorithmic regularity for graphs with general degree distributions. In Automata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings (pp. 789-800). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4596 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-73420-8_68

Alon, Noga ; Coja-Oghlan, Amin ; Hàn, Hiêp et al. / Quasi-randomness and algorithmic regularity for graphs with general degree distributions. Automata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings. Springer Verlag, 2007. pp. 789-800 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We deal with two very related subjects: quasi-randomness and regular partitions. The purpose of the concept of quasi-randomness is to measure how much a given graph {"}resembles{"} a random one. Moreover, a regular partition approximates a given graph by a bounded number of quasi-random graphs. Regarding quasi-randomness, we present a new spectral characterization of low discrepancy, which extends to sparse graphs. Concerning regular partitions, we present a novel concept of regularity that takes into account the graph's degree distribution, and show that if G = (V, E) satisfies a certain boundedness condition, then G admits a regular partition. In addition, building on the work of Alon and Naor [4], we provide an algorithm that computes a regular partition of a given (possibly sparse) graph G in polynomial time.",

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Alon, N, Coja-Oghlan, A, Hàn, H, Kang, M, Rödl, V & Schacht, M 2007, Quasi-randomness and algorithmic regularity for graphs with general degree distributions. in Automata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4596 LNCS, Springer Verlag, pp. 789-800, 34th International Colloquium on Automata, Languages and Programming, ICALP 2007, Wroclaw, Poland, 9/07/07. https://doi.org/10.1007/978-3-540-73420-8_68

Quasi-randomness and algorithmic regularity for graphs with general degree distributions. / Alon, Noga; Coja-Oghlan, Amin; Hàn, Hiêp et al.
Automata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings. Springer Verlag, 2007. p. 789-800 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4596 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We deal with two very related subjects: quasi-randomness and regular partitions. The purpose of the concept of quasi-randomness is to measure how much a given graph "resembles" a random one. Moreover, a regular partition approximates a given graph by a bounded number of quasi-random graphs. Regarding quasi-randomness, we present a new spectral characterization of low discrepancy, which extends to sparse graphs. Concerning regular partitions, we present a novel concept of regularity that takes into account the graph's degree distribution, and show that if G = (V, E) satisfies a certain boundedness condition, then G admits a regular partition. In addition, building on the work of Alon and Naor [4], we provide an algorithm that computes a regular partition of a given (possibly sparse) graph G in polynomial time.

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Alon N, Coja-Oghlan A, Hàn H, Kang M, Rödl V, Schacht M. Quasi-randomness and algorithmic regularity for graphs with general degree distributions. In Automata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings. Springer Verlag. 2007. p. 789-800. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-73420-8_68

Quasi-randomness and algorithmic regularity for graphs with general degree distributions

Abstract

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Keywords

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