Browse > Article
http://dx.doi.org/10.9708/jksci.2015.20.3.107

An Algorithm for Minimum Feedback Edge Set Problem  

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.3, 2015 , pp. 107-113 More about this Journal
Abstract
This paper presents a polynomial time algorithm to the minimum cardinality feedback edge set and minimum weight feedback edge set problems. The algorithm makes use of the property wherein the sum of the minimum spanning tree edge set and the minimum feedback edge set equals a given graph's edge set. In other words, the minimum feedback edge set is inherently a complementary set of the former. The proposed algorithm, in pursuit of the optimal solution, modifies the minimum spanning tree finding Kruskal's algorithm so as to arrange the weight of edges in a descending order and to assign cycle-deficient edges to the maximum spanning tree edge set MXST and cycle-containing edges to the feedback edge set FES. This algorithm runs with linear time complexity, whose execution time corresponds to the number of edges of the graph. When extensively tested on various undirected graphs both with and without the weighed edge, the proposed algorithm has obtained the optimal solutions with 100% success and accuracy.
Keywords
Minimum feedback edge set problem; Weight; Cardinality; Minimum spanning tree;
Citations & Related Records
연도 인용수 순위
  • Reference
1 P. Festa, P. M. Pardalos, and M. G. C. Resende, "Feedback Set Problems," AT&T Labs Research Technical Report: 99.2.2, http://www.research.att.com/-mgcr/doc/sfsp,pdf, 1999.
2 Wikipedia, "Feedback Vertex Set," http://en.wikipedia.org/wiki/Feedback_vertex_set, Wikimedia Foundation Inc., 2014.
3 Wikipedia, "Feedback Arc Set," http://en.wikipedia.org/wiki/Feedback_arc_set,Wikimedia Foundation Inc., 2014.
4 T. C. Dijk, "Kernelization For Cutset," The 19th Belgian-DutchConference onArtificial Intelligence (BNAIC 2007), http://people.cs.uu.nl/thomasd/bnaickernel.ppt, 2007.
5 Y-L. Chen, "On the Study of Feedback Problems in Diamond Graphs," InformationManagement, National Ch-Nan University, Master Thesis, 2006.
6 C. Demetrescu and I. Finocchi, "Combinatorial Algorithms for Feedback Problems," Information Processing Letters (IPL), Vol. 86, No. 3, pp. 129-139, May. 2003.   DOI   ScienceOn
7 Wikipedia, "Minimum Spanning Tree," http://en.wikipedia.org/wiki/Minimum_spanning_tree,Wikimedia Foundation, Inc., 2014.
8 J. B. Kruskal, "On the Shortest Spanning Subtree and The Traveling Salesman Problem," Proceedings of the AmericanMathematical Society, Vol. 7, No. 1, pp. 48-50, Feb. 1956.
9 WWL. Chen, "DiscreteMathematics," Department of Mathematics, Division of ICS, Macquarie University, Australia,http://www.maths.mq.edu.au/-wchen/lndmfolder/lndm.html, 2003.
10 A. Saha andM. Pal, "AnAlgorithmto find aMinimum Feedback Vertex Set of an Interval Graph," Advanced Modeling and Optimization, Vol. 7, No. 1, pp. 99-116, Jan. 2005.
11 K. Cattell, M. J. Dinneen and M. R. Fellows, "Obstructions to within a few vertices or edges of acyclic," 4th InternationalWorkshop on Algorithms and Data Structures, Springer-Verlag, Lecture Notes in Computer Science, Vol. 955, pp. 415-427, Jun. 1995.