Adjacency labeling schemes and induced-universal graphs

Stephen Alstrup; Haim Kaplan; Mikkel Thorup; Uri Zwick

doi:10.1145/2746539.2746545

Adjacency labeling schemes and induced-universal graphs

Stephen Alstrup, Haim Kaplan, Mikkel Thorup, Uri Zwick

School of Computer Science

University of Copenhagen

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

33 Scopus citations

Abstract

We describe a way of assigning labels to the vertices of any undirected graph on up to n vertices, each composed of n/2+ O(1) bits, such that given the labels of two vertices, and no other information regarding the graph, it is possible to decide whether or not the vertices are adjacent in the graph. This is optimal, up to an additive constant, and constitutes the first improvement in almost 50 years of an n/2+O(log n) bound of Moon. As a consequence, we obtain an induced-universal graph for n-vertex graphs containing only O(2^n/2) vertices, which is optimal up to a multiplicative constant, solving an open problem of Vizing from 1968. We obtain similar tight results for directed graphs, tournaments and bipartite graphs.

Original language	English
Title of host publication	STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing
Publisher	Association for Computing Machinery
Pages	625-634
Number of pages	10
ISBN (Electronic)	9781450335362
DOIs	https://doi.org/10.1145/2746539.2746545
State	Published - 14 Jun 2015
Event	47th Annual ACM Symposium on Theory of Computing, STOC 2015 - Portland, United States Duration: 14 Jun 2015 → 17 Jun 2015

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
Volume	14-17-June-2015
ISSN (Print)	0737-8017

Conference

Conference	47th Annual ACM Symposium on Theory of Computing, STOC 2015
Country/Territory	United States
City	Portland
Period	14/06/15 → 17/06/15

Keywords

Adjacency labeling schemes
Induced-universal graphs

Access to Document

10.1145/2746539.2746545

Cite this

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title = "Adjacency labeling schemes and induced-universal graphs",

abstract = "We describe a way of assigning labels to the vertices of any undirected graph on up to n vertices, each composed of n/2+ O(1) bits, such that given the labels of two vertices, and no other information regarding the graph, it is possible to decide whether or not the vertices are adjacent in the graph. This is optimal, up to an additive constant, and constitutes the first improvement in almost 50 years of an n/2+O(log n) bound of Moon. As a consequence, we obtain an induced-universal graph for n-vertex graphs containing only O(2n/2) vertices, which is optimal up to a multiplicative constant, solving an open problem of Vizing from 1968. We obtain similar tight results for directed graphs, tournaments and bipartite graphs.",

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Alstrup, S, Kaplan, H, Thorup, M & Zwick, U 2015, Adjacency labeling schemes and induced-universal graphs. in STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, vol. 14-17-June-2015, Association for Computing Machinery, pp. 625-634, 47th Annual ACM Symposium on Theory of Computing, STOC 2015, Portland, United States, 14/06/15. https://doi.org/10.1145/2746539.2746545

Adjacency labeling schemes and induced-universal graphs. / Alstrup, Stephen; Kaplan, Haim; Thorup, Mikkel et al.
STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing. Association for Computing Machinery, 2015. p. 625-634 (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. 14-17-June-2015).

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

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AB - We describe a way of assigning labels to the vertices of any undirected graph on up to n vertices, each composed of n/2+ O(1) bits, such that given the labels of two vertices, and no other information regarding the graph, it is possible to decide whether or not the vertices are adjacent in the graph. This is optimal, up to an additive constant, and constitutes the first improvement in almost 50 years of an n/2+O(log n) bound of Moon. As a consequence, we obtain an induced-universal graph for n-vertex graphs containing only O(2n/2) vertices, which is optimal up to a multiplicative constant, solving an open problem of Vizing from 1968. We obtain similar tight results for directed graphs, tournaments and bipartite graphs.

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Adjacency labeling schemes and induced-universal graphs

Abstract

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Conference

Keywords

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