Abstract
Given a connected, edge-weighted and undirected complete graph G(V, E, w), and a positive integer d, the degree-constrained minimum spanning tree (dc-MST) problem aims to find a spanning tree of minimum cost in such a way that the degree of each node in T is at most d. The dc-MST problem is a \(\mathcal {NP}\)-Hard problem. In this paper, we propose a problem-specific heuristic (\(\mathcal {H}\_\)DCMST) for the dc-MST problem. \(\mathcal {H}\_\)DCMST consists of two phases, where the first phase constructs a degree-constrained spanning tree (T) and the second phase examines the edges of T for possible exchange in two stages followed one-by-one in order to further reduce the cost of T. On a number of TSP benchmark instances, the proposed \(\mathcal {H}\_\)DCMST has been compared with the heuristic BF2 proposed by Boldon et al. (Parallel Comput. 22(3):369–382, 1996) [3] for constructing spanning trees with d = 3. Computational experiments show the effectiveness of the proposed \(\mathcal {H}\_\)DCMST.
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Acknowledgements
This work is supported by the Science and Engineering Research Board—Department of Science & Technology, Government of India [grant no.: YSS/2015/000276].
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Singh, K., Sundar, S. (2019). A Heuristic for the Degree-Constrained Minimum Spanning Tree Problem. In: Ray, K., Sharma, T., Rawat, S., Saini, R., Bandyopadhyay, A. (eds) Soft Computing: Theories and Applications. Advances in Intelligent Systems and Computing, vol 742. Springer, Singapore. https://doi.org/10.1007/978-981-13-0589-4_33
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DOI: https://doi.org/10.1007/978-981-13-0589-4_33
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