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

Department of Computer Science

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

33 Citations (Scopus)

Abstract

We show that there exists a graph $G$ with $\Oh(n)$ nodes, where any forest of $n$ nodes is a node-induced subgraph of $G$. Furthermore, for constant arboricity $k$, the result implies the existence of a graph with $\Oh(n^k)$ nodes that contains all $n$-node graphs as node-induced subgraphs, matching a $\Omega(n^k)$ lower bound. The lower bound and previously best upper bounds were presented in Alstrup and Rauhe (FOCS'02). Our upper bounds are obtained through a $\log_2 n +\Oh(1)$ labeling scheme for adjacency queries in forests.

We hereby solve an open problem being raised repeatedly over decades, e.g. in Kannan, Naor, Rudich (STOC 1988), Chung (J. of Graph Theory 1990), Fraigniaud and Korman (SODA 2010).

Original language	English
Title of host publication	Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC 2015, Portland, OR, USA, June 14-17, 2015 : STOC '15
Number of pages	10
Publisher	Association for Computing Machinery
Publication date	2015
Pages	625-634
ISBN (Print)	978-1-4503-3536-2
DOIs	https://doi.org/10.1145/2746539.2746545
Publication status	Published - 2015
Event	Annual ACM Symposium on the Theory of Computing 2015 - Portland, United States Duration: 15 Jun 2015 → 17 Jun 2015 Conference number: 47

Conference

Conference	Annual ACM Symposium on the Theory of Computing 2015
Number	47
Country/Territory	United States
City	Portland
Period	15/06/2015 → 17/06/2015

Access to Document

10.1145/2746539.2746545

Adjacency Labeling Schemes and Induced-Universal GraphsFinal published version, 887 KB

Cite this

Adjacency labeling schemes and induced-universal graphs. / Alstrup, Stephen; Kaplan, Haim; Thorup, Mikkel; Zwick, Uri.

Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC 2015, Portland, OR, USA, June 14-17, 2015: STOC '15. Association for Computing Machinery, 2015. p. 625-634.

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

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

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