On the interval completion of chordal graphs

Authors:
Sheng-Lung Peng;Chi-Kang Chen
Affiliations:
Department of Computer Science and Information Engineering, National Dong Hwa University, Hualien, Taiwan 974, ROC;Department of Computer Science and Information Engineering, National Dong Hwa University, Hualien, Taiwan 974, ROC
Venue:
Discrete Applied Mathematics
Year:
2006

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Abstract

For a given graph G=(V,E), the interval completion problem of G is to find an edge set F such that the supergraph H=(V,E@?F) of G is an interval graph and |F| is minimum. It has been shown that it is equivalent to the minimum sum cut problem, the profile minimization problem and a kind of graph searching problems. Furthermore, it has applications in computational biology, archaeology, and clone fingerprinting. In this paper, we show that it is NP-complete on split graphs and propose an efficient algorithm on primitive starlike graphs.