Abstract
The degree-constrained minimum spanning tree (DCMST) problem seeks a spanning tree T of minimum cost on a given connected, weighted and undirected complete graph in such a way that the degree of each vertex in T should not exceed d, where d is a positive integer. The DCMST is a \(\mathcal {NP}\)-Hard problem for d \(\ge \) 2. This paper presents a new problem-specific heuristic (\(\mathcal {H}eu\_\)DCMST). \(\mathcal {H}eu\_\)DCMST first builds a feasible degree-constrained spanning tree (T) with the help of problem-specific knowledge of the DCMST problem, then it further tries to reduce the cost of T through edge-exchange. On a number of TSP benchmark instances, the proposed \(\mathcal {H}eu\_\)DCMST has been compared with the heuristic proposed by Boldon et al. [3] and demonstrates its effectiveness.
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Acknowledgements
This work is supported by the Science and Engineering Research Board-Department of Science & Technology, Government of India [grant number: YSS/2015/000276].
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Singh, K., Sundar, S. (2019). A New Heuristic for Degree-Constrained Minimum Spanning Tree Problem. In: Verma, N., Ghosh, A. (eds) Computational Intelligence: Theories, Applications and Future Directions - Volume I. Advances in Intelligent Systems and Computing, vol 798. Springer, Singapore. https://doi.org/10.1007/978-981-13-1132-1_12
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DOI: https://doi.org/10.1007/978-981-13-1132-1_12
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