On the hardness of optimal vertex relabeling and restricted vertex relabeling

Amihood Amir; Benny Porat

doi:10.1007/978-3-319-19929-0_1

On the hardness of optimal vertex relabeling and restricted vertex relabeling

Amihood Amir
, Benny Porat

Department of Computer Science

Johns Hopkins University

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

3 Scopus citations

Abstract

Vertex Relabeling is a variant of the graph relabeling problem. In this problem, the input is a graph and two vertex labelings, and the question is to determine how close are the labelings. The distance measure is the minimum number of label swaps necessary to transform the graph from one labeling to the other, where a swap is the interchange of the labels of two adjacent nodes. We are interested in the complexity of determining the swap distance. The problem has been recently explored for various restricted classes of graphs, but its complexity in general graphs has not been established. We show that the problem is NP-hard. In addition we consider restricted versions of the problem where a node can only participate in a bounded number of swaps. We show that the problem is NP-hard under these restrictions as well.

Original language	English
Title of host publication	Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings
Editors	Ugo Vaccaro, Ely Porat, Ferdinando Cicalese
Publisher	Springer Verlag
Pages	1-12
Number of pages	12
ISBN (Print)	9783319199283
DOIs	https://doi.org/10.1007/978-3-319-19929-0_1
State	Published - 2015
Event	26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015 - Ischia Island, Italy Duration: 29 Jun 2015 → 1 Jul 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9133
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015
Country/Territory	Italy
City	Ischia Island
Period	29/06/15 → 1/07/15

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2015.

Funding

B. Porat—Partly supported by a Bar Ilan University President Fellowship. This work is part of Benny Porat’s Ph.D. thesis. A. Amir—Partly supported by ISF grant 571/14.

Funders	Funder number
Israel Science Foundation
Bar-Ilan University
Israel Science Foundation	571/14

Access to Document

10.1007/978-3-319-19929-0_1

Cite this

Amir, A., & Porat, B. (2015). On the hardness of optimal vertex relabeling and restricted vertex relabeling. In U. Vaccaro, E. Porat, & F. Cicalese (Eds.), Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings (pp. 1-12). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9133). Springer Verlag. https://doi.org/10.1007/978-3-319-19929-0_1

Amir, Amihood ; Porat, Benny. / On the hardness of optimal vertex relabeling and restricted vertex relabeling. Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. editor / Ugo Vaccaro ; Ely Porat ; Ferdinando Cicalese. Springer Verlag, 2015. pp. 1-12 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Amir, A & Porat, B 2015, On the hardness of optimal vertex relabeling and restricted vertex relabeling. in U Vaccaro, E Porat & F Cicalese (eds), Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9133, Springer Verlag, pp. 1-12, 26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015, Ischia Island, Italy, 29/06/15. https://doi.org/10.1007/978-3-319-19929-0_1

On the hardness of optimal vertex relabeling and restricted vertex relabeling. / Amir, Amihood; Porat, Benny.
Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. ed. / Ugo Vaccaro; Ely Porat; Ferdinando Cicalese. Springer Verlag, 2015. p. 1-12 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9133).

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

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Amir A, Porat B. On the hardness of optimal vertex relabeling and restricted vertex relabeling. In Vaccaro U, Porat E, Cicalese F, editors, Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. Springer Verlag. 2015. p. 1-12. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-19929-0_1

On the hardness of optimal vertex relabeling and restricted vertex relabeling

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