Feedback vertex sets in rotator graphs

Authors:
Chiun-Chieh Hsu;Hon-Ren Lin;Hsi-Cheng Chang;Kung-Kuei Lin
Affiliations:
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, Hwa-Shia Institute of Technology, Taipei, Taiwan, ROC;Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan, ROC
Venue:
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part V
Year:
2006

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Abstract

This paper provides an algorithm for finding feedback vertex set in rotator graphs. Feedback vertex set is a subset of a graph whose removal causes an acyclic graph and is developed in various topologies of interconnected networks. In 1992, Corbett pioneered rotator graphs, whose interesting topological structures attract many researchers to publish relative papers in recent years. In this paper, we first develops feedback vertex set algorithm for rotator graphs. Our algorithm utilizes the technique of dynamic programming and generates a feedback vertex set of size n!/3 for a rotator graph of scale n, which contains n! nodes. The generated set size is proved to be minimum. Finding a minimum feedback vertex set is a NP-hard problem for general graphs. The time complexity of our algorithm, which finds a minimum feedback vertex set for a rotator graph of scale n, is proved to be O(nn−−3).