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All Colors Shortest Path problem on trees.
- Source :
- Journal of Heuristics; Aug2018, Vol. 24 Issue 4, p617-644, 28p
- Publication Year :
- 2018
-
Abstract
- Given an edge weighted tree T(V, E), rooted at a designated base vertex r∈V<inline-graphic></inline-graphic>, and a color from a set of colors C={1,…,k}<inline-graphic></inline-graphic> assigned to every vertex v∈V<inline-graphic></inline-graphic>, 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 13811231
- Volume :
- 24
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Journal of Heuristics
- Publication Type :
- Academic Journal
- Accession number :
- 130723285
- Full Text :
- https://doi.org/10.1007/s10732-018-9370-4