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All Colors Shortest Path problem on trees

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Abstract

Given an edge weighted tree T(V, E), rooted at a designated base vertex \(r \in V\), and a color from a set of colors \(C=\{1,\ldots ,k\}\) assigned to every vertex \(v \in V\), All Colors Shortest Path problem on trees (ACSP-t) seeks the shortest, possibly non-simple, path starting from r in T such that at least one node from every distinct color in C is visited. We show that ACSP-t is NP-hard, and also prove that it does not have a constant factor approximation. We give an integer linear programming formulation of ACSP-t. Based on a linear programming relaxation of this formulation, an iterative rounding heuristic is proposed. The paper also explores genetic algorithm and tabu search to develop alternative heuristic solutions for ACSP-t. The performance of all the proposed heuristics are evaluated experimentally for a wide range of trees that are generated parametrically.

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Authors and Affiliations

  1. Department of Software Engineering, Izmir University of Economics, 35330, Izmir, Turkey

    Mehmet Berkehan Akçay & Hüseyin Akcan

  2. Department of Computer Engineering, Izmir University of Economics, 35330, Izmir, Turkey

    Cem Evrendilek

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  1. Mehmet Berkehan Akçay
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  2. Hüseyin Akcan
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  3. Cem Evrendilek
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Correspondence to Hüseyin Akcan.

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Akçay, M.B., Akcan, H. & Evrendilek, C. All Colors Shortest Path problem on trees. J Heuristics 24, 617–644 (2018). https://doi.org/10.1007/s10732-018-9370-4

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  • DOI: https://doi.org/10.1007/s10732-018-9370-4

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