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On the Hardness of Optimal Vertex Relabeling and Restricted Vertex Relabeling

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Combinatorial Pattern Matching (CPM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9133))

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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 \(\mathcal {NP}\)-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 \(\mathcal {NP}\)-hard under these restrictions as well.

A. Amir—Partly supported by ISF grant 571/14.

B. Porat—Partly supported by a Bar Ilan University President Fellowship. This work is part of Benny Porat’s Ph.D. thesis.

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Authors and Affiliations

  1. Department of Computer Science, Bar-Ilan University, 52900, Ramat-gan, Israel

    Amihood Amir & Benny Porat

  2. Department of Computer Science, Johns Hopkins University, Baltimore, MD, 21218, USA

    Amihood Amir

Authors
  1. Amihood Amir
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  2. Benny Porat
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Correspondence to Amihood Amir .

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Editors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Ferdinando Cicalese

  2. Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel

    Ely Porat

  3. Department of Computer Science, University of Salerno, Fisciano, Italy

    Ugo Vaccaro

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Amir, A., Porat, B. (2015). On the Hardness of Optimal Vertex Relabeling and Restricted Vertex Relabeling. In: Cicalese, F., Porat, E., Vaccaro, U. (eds) Combinatorial Pattern Matching. CPM 2015. Lecture Notes in Computer Science(), vol 9133. Springer, Cham. https://doi.org/10.1007/978-3-319-19929-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-19929-0_1

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  • Online ISBN: 978-3-319-19929-0

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