Abstract
There are a number of algorithms that have been proposed in the graph theory literature to compute the minimum spanning tree of a given graph. These include the famous Prim’s and Kruskal’s algorithm, among others. The main drawback of these algorithms is their greedy nature, which means they cannot be applied to large datasets. In 2015, Zhong et al. proposed a fast MST (FMST) algorithm framework that uses K-means to find the MST with a reduced complexity of O(N1.5). In this paper, we have introduced an improved version of the FMST algorithm by using K-means++ to further increase the efficiency of the FMST algorithm. The use of K-means++ instead of K-means results in lesser complexity, faster convergence, and more accurate results during the clustering step which improves the accuracy of the MST formed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Arthur, D., Vassilvitskii, S.: k-means++: The advantages of careful seeding. In SODA, pages 1027–1035 (2007).
Bahmani, B., Moseley, B., Vattani, A., Kumar, R., Vassilvitskii, S.: Scalable k-means++, Proceedings of the VLDB Endowment 5.7, 622–633(2012).
Cheriton, D., Tarjan, R.E.: Finding minimum spanning trees, SIAM J. Comput. 5 24–742 (1976).
Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms, J. ACM, 34, 596–615(1987).
Gabow, H.N., Galil, Z., Spencer, T.H., Tarjan, R.E.: Efficient algorithms for finding minimum spanning trees in undirected and directed graphs, Combinatorica, 6 109–122(1986).
https://github.com/deric/clustering-benchmark/tree/master/src/main/resources/datasets/artificial.
Karypis, G., Han, E.H., Kumar, V.: CHAMELEON: a hierarchical clustering algorithm using dynamic modeling, IEEE Trans. Comput. 32 68–75(1999).
Kruskal, J. B.: On the shortest spanning subtree of a graph and the travelling salesman problem, Proc. Amer. Math. Soc. 7, 48–50 (1956).
Nesetril, J., Milkova, E., Nesetrilov, H.: Otakar Boruvka on minimum spanning tree problem – Translation of both the 1926 papers, comments, history, Discrete Mathematics, 233, 3–36 (2001).
Prim, R. C.: The shortest connecting network and some generalization, Bell Systems Tech. J. 36, 1389–1401(1957),
Yao, A.C.: An O(E log log V) algorithm for finding minimum spanning trees, Inform. Process. Lett. 4, 21–23(1975).
Zhong, C., Malinen, M., Miao, D. and Fränti, P.: A fast minimum spanning tree algorithm based on K-means. Information Sciences 295, 1–17(2015).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Sandhu, S.S., Tripathy, B.K., Jagga, S. (2019). KMST+: A K-Means++-Based Minimum Spanning Tree Algorithm. In: Panigrahi, B., Trivedi, M., Mishra, K., Tiwari, S., Singh, P. (eds) Smart Innovations in Communication and Computational Sciences. Advances in Intelligent Systems and Computing, vol 669. Springer, Singapore. https://doi.org/10.1007/978-981-10-8968-8_10
Download citation
DOI: https://doi.org/10.1007/978-981-10-8968-8_10
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-8967-1
Online ISBN: 978-981-10-8968-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)