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Journal of Heuristics

, Volume 24, Issue 4, pp 617–644 | Cite as

All Colors Shortest Path problem on trees

  • Mehmet Berkehan Akçay
  • Hüseyin Akcan
  • Cem Evrendilek
Article

Abstract

Given an edge weighted tree T(VE), 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.

Keywords

NP-hardness Inapproximability Integer linear programming Linear programming relaxation Genetic algorithm Tabu search 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Software EngineeringIzmir University of EconomicsIzmirTurkey
  2. 2.Department of Computer EngineeringIzmir University of EconomicsIzmirTurkey

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