A Solution of Degree Constrained Spanning Tree Using Hybrid GA with Directed Mutation

  • Sounak Sadhukhan
  • Samar Sen Sarma
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 27)


It is always an urge to reach the goal in minimum effort i.e., it should have a minimum constrained path. The path may be shortest route in practical life, either physical or electronic medium. The scenario can be represented as a graph. Here, we have chosen a degree constrained spanning tree, which can be generated in real time in minimum turn-around time. The problem is obviously NP-complete in nature. The solution approach, in general, is approximate. We have used a heuristic approach, namely hybrid genetic algorithm (GA), with motivated criteria of encoded data structures of graph and also directed mutation is incorporated with it and the result is so encouraging, that we are interested to use it in our future applications.


NP-complete degree constrained spanning tree graphical edge-set representation graphical edge-set crossover graphical edge-set directed mutation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Rosen, K.H.: Discrete Mathematics and its Application.TMH Edition (2000)Google Scholar
  2. 2.
    SenSarma, S., Dey, K.N., Naskar, S., Basuli, K.: A Close Encounter with Intractability. Social Science Research Network (2009)Google Scholar
  3. 3.
    Raidl, R.G.: An Efficient Evolutionary Algorithm for the Degree Constrained Minimum Spanning Tree Problem. In: Proceedings of the 2000 Congress on Evolutionary Computation, pp. 104–111 (2000)Google Scholar
  4. 4.
    Garey, M.R., Johnson, D.S.: Computers and Intractability – A guide to the Theory of NP Completeness. W.H. Freeman and Company (1999)Google Scholar
  5. 5.
    Narula, S.C., Ho, C.A.: Degree-constrained minimum spanning tree. Computers and Operations Research 7, 239–249 (1980)Google Scholar
  6. 6.
    Zhou, G., Gen, M., Wut, T.: A New Approach to the Degree-Constrained Minimum Spanning Tree Problem Using Genetic Algorithm. In: IEEEInternational Conference on Systems, Man and Cybernetics, pp. 2683–2688 (1996)Google Scholar
  7. 7.
    Knowles, J., Corne, D.: A New Evolutionary Approach to the Degree-Constrained Mini-mum Spanning Tree Problem. IEEE Transaction on Evolutionary Computation 4, 125–134 (2000)CrossRefGoogle Scholar
  8. 8.
    Zeng, Y., Wang, Y.: A New Genetic Algorithm with Local Search Method for Degree-Constrained Minimum Spanning Tree problem. In: IEEE International Conference on Computational Intelligence and Multimedia Applications, pp. 218–222 (2003)Google Scholar
  9. 9.
    Zhou, G., Meng, Z., Cao, Z., Cao, J.: A New Tree Encoding for the Degree-Constrained Spanning Tree Problem. In: IEEE International Conference on Computational Intelligence and Security, pp. 85–90 (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringUniversity of CalcuttaKolkataIndia

Personalised recommendations