Abstract
For a given graph \(G\), minimum stretch spanning tree problem (MSSTP) seeks for a spanning tree of \(G\) such that the distance between the farthest pair of adjacent vertices of \(G\) in tree is minimized. It is an NP-hard problem with applications in communication networks. In this paper, a general variable neighborhood search (GVNS) algorithm is developed for MSSTP in which initial solution is generated using four well-known heuristics and a problem-specific construction heuristic. Six neighborhood strategies are designed to explore the search space. The experiments are conducted on various classes of graphs for which optimal results are known. Computational results show that the proposed algorithm is better than the artificial bee colony (ABC) algorithm which is adapted by us for MSSTP.
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References
Mladenovic N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24(11):1097–1100
Hansen P, Mladenovic N, Perez JAM (2010) Variable neighbourhood search: methods and applications. Ann Oper Res 175(1):367–407
Sanchez-Oro J, Pantrigo JJ, Duarte A (2014) Combining intensification and diversification strategies in VNS. An application to the Vertex Separation problem. Comput Oper Res 52:209–219
Peleg D, Ullman JD (1989) An optimal synchronizer for the hypercube. SIAM J Comput 18(4):740–747
Liebchen C, Wunsch G (2008) The zoo of tree spanner problems. Discrete Appl Math 156(5):569–587
Cai L, Corneil DG (1995) Tree spanners. SIAM J Discrete Math 8(3):359–387
Singh K, Sundar S (2018) Artificial bee colony algorithm using problem-specific neighborhood strategies for the tree t-spanner problem. Appl Soft Comput 62:110–118
Boksberger P, Kuhn F, Wattenhofer R (2003) On the approximation of the minimum maximum stretch tree problem. Technical report 409
Lin L, Lin Y (2017) The minimum stretch spanning tree problem for typical graphs. arXiv preprint arXiv:1712.03497
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Kardam, Y.S., Srivastava, K. (2021). General Variable Neighborhood Search for the Minimum Stretch Spanning Tree Problem. In: Singh, V., Asari, V., Kumar, S., Patel, R. (eds) Computational Methods and Data Engineering. Advances in Intelligent Systems and Computing, vol 1227. Springer, Singapore. https://doi.org/10.1007/978-981-15-6876-3_12
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DOI: https://doi.org/10.1007/978-981-15-6876-3_12
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