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Characterization of interval graphs that are paired 2-disjoint path coverable

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Abstract

The performance of a supercomputing system is significantly affected by the network used to interconnect the nodes. One of the key problems associated with parallel processing is finding disjoint paths in the underlying graph of an interconnection network. It is often important to find disjoint paths that collectively pass through all the vertices. A disjoint path cover of a graph is a set of vertex-disjoint paths that altogether cover every vertex of the graph. Given disjoint source and sink sets, \(S = \{ s_1,\ldots ,s_k\}\) and \(T = \{t_1,\ldots , t_k\}\), in a graph, a paired k-disjoint path cover joining S and T is a disjoint path cover \(\{ P_1, \ldots , P_k\}\) composed of k paths, in which each path \(P_i\) runs from \(s_i\) to \(t_i\). In this paper, we characterize interval graphs that have a paired 2-disjoint path cover joining S and T for any possible configurations of source and sink sets S and T of size 2 each.

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Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1F1A1048180). This work was also supported by the Catholic University of Korea, Research Fund, 2020.

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Authors and Affiliations

  1. School of Computer Science and Information Engineering, The Catholic University of Korea, Bucheon City, Republic of Korea

    Jung-Heum Park

  2. Department of Software Engineering, Chonnam National University, Gwangju, Republic of Korea

    Hyeong-Seok Lim

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  1. Jung-Heum Park
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Correspondence to Jung-Heum Park.

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Park, JH., Lim, HS. Characterization of interval graphs that are paired 2-disjoint path coverable. J Supercomput 79, 2783–2800 (2023). https://doi.org/10.1007/s11227-022-04768-x

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