Browse > Article
http://dx.doi.org/10.9708/jksci.2015.20.5.031

A Degree-Constrained Minimum Spanning Tree Algorithm Using k-opt  

Lee, Sang-Un (Dept. of Multimedia Eng., Gangneung-Wonju National University)
Publication Information
Journal of the Korea Society of Computer and Information / v.20, no.5, 2015 , pp. 31-39 More about this Journal
Abstract
The degree-constrained minimum spanning tree (d-MST) problem is considered NP-complete for no exact solution-yielding polynomial algorithm has been proposed to. One thus has to resort to an heuristic approximate algorithm to obtain an optimal solution to this problem. This paper therefore presents a polynomial time algorithm which obtains an intial solution to the d-MST with the help of Kruskal's algorithm and performs k-opt on the initial solution obtained so as to derive the final optimal solution. When tested on 4 graphs, the algorithm has successfully obtained the optimal solutions.
Keywords
Minimum spanning tree; Degree constrained; Hamiltonian path; k-opt edge swap;
Citations & Related Records
연도 인용수 순위
  • Reference
1 O. Boruvka, "O Jistem Problemu Minimalnim," Prace Mor. Prrodved. Spol. V Brne (Acta Societ. Natur. Moravicae), Vol. III, No. 3, pp. 37-58, Mar. 1926.
2 J. Nesetril, E. Milkova, and H. Nesetrilova, "Otakar Boruvka on Minimum Spanning Tree Problem (Translation of the both 1926 Papers, Comments, History)," DMATH: DiscreteMathematics, Vol. 233, No. 1-3, Apr. 2001.
3 R. C. Prim, "Shortest Connection Networks and Some Generalisations," Bell SystemTechnical Journal, Vol. 36, No. 6, pp. 1389-1401, Nov. 1957.
4 J. B. Kruskal, "On the Shortest Spanning Subtree and The Traveling Salesman Problem," Proceedings of the American Mathematical Society, Vol. 7, pp. 48-50, 1956.
5 Wikipedia, "Minimum Spanning Tree," http://en.wikipedia.org/wiki/Minimum_spanning_tree, 2014.
6 Wikipedia, "Degree-constrained Spanning Tree," http://en.wikipedia.org/wiki/Degree-constrained_Spanning_Tree, 2014.
7 G. R. Raidl, "An Efficient Evolutionary Algorithmfor the Degree-Constrained Minimum Spanning Tree Problem," Proceedings of the 2000 IEEE Congress on Evolutionary Computation, pp. 104-111, IEEE Press, 2000.
8 S. C. Narula and C. A. Ho, "Degree-Constrained Minimum Spanning Tree," Computational Operations Research, Vol. 7, pp. 239-249, 1980.   DOI   ScienceOn
9 M. Gen, "Evolutionary Algorithms and Optimization: Theory and Its Application," Software Computing Lab., Waseda University, IPS., 2004.
10 C. H. Chu, G. Premkumar, C. Chou, and J. Sun, "Dynamic Degree Constrained Network Design: A Genetic Algorithm Approach," School of Computer Science, University of Birmingham, UK., 1999.
11 G. Zhou and M. Gen, "A Note on Genetic Algorithms for Degree-Constrained Spanning Tree Problems," Networks, Vol. 30, No. 2, pp. 91-95, Sep. 1997.   DOI
12 J. Knowles, D. Corne, and M. Oates, "A New Evolutionary Approach to the Degree Constrained Minimum Spanning Tree Problem," Trans. on Evolutionary Computation, Vol. 4, No. 2, pp. 125-134, Jul. 2000.   DOI   ScienceOn
13 X. Duan, C. Wang, X. Lue, and N. Wang, "AHybrid Algorithm Based on Particle Swarm Optimization," International Journal of Information and Systems Science, Vol. 1, No. 3-4, pp. 275-282, Apr. 2005.
14 L. Gouveia and P. Moura, "Models for the Degree Constrained Minimum Spanning Tree Problem with Node-Degree Dependent Costs," International Network Optimization Conference, Spa, Belgium, 2007.
15 M. Krishnamoorthy, A. T. Ernst, and Y. M. Sharaiha, "Comparison of Algorithms for the Degree Constrained Minimum Spanning Tree," Journal of Heuristics, Vol. 7, No. 6, pp. 587-611, Nov. 2001.   DOI
16 L. Stougie, "2P350: Optimaliseringsmethoden," http://www.win.tue.nl/-leen/OW/2P350/Week8/week8.pdf, College Wordt ggeven op vinjdagmiddag, 2001.
17 G. Zhou and M. Gen, "Approach to the Degree-Constrained Minimum Spanning Tree Problem Using Genetic Algorithms," Engineering Design and Automation, Vol. 3, No. 2, pp. 156-165, Feb. 1997.
18 M. Savelsbergh and T. Volgenant, "Edge-Exchanges in the Degree-Constrained Minimum Spanning Tree Problem," Computers and Operations Research, Vol. 12, No. 4, pp. 341-348, Apr. 1985.   DOI   ScienceOn