An efficient algorithm for minimum feedback vertex sets in rotator graphs

Authors:
Chi-Jung Kuo;Chiun-Chieh Hsu;Hon-Ren Lin;Kung-Kuei Lin
Affiliations:
Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan, ROC;Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan, ROC;Department of Information Management, National Taipei College of Business, Taipei, Taiwan, ROC;Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan, ROC
Venue:
Information Processing Letters
Year:
2009

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Abstract

For a rotator graph with n! nodes, Hsu and Lin [C.C. Hsu, H.R. Lin, H.C. Chang, K.K. Lin, Feedback Vertex Sets in Rotator Graphs, in: Lecture Notes in Comput. Sci., vol. 3984, 2006, pp. 158-164] first proposed an algorithm which constructed a feedback vertex set (FVS) with time complexity O(n^n^-^3). In addition, they found that the size of the FVS is n!/3, which was proved to be minimum. In this paper, we present an efficient algorithm which constructs an FVS for a rotator graph in O(n!) time and also obtains the minimum FVS size n!/3. In other words, this algorithm derives the optimal result with linear time complexity in terms of the number of nodes in the rotator graph.