Improved algorithms for weakly chordal graphs

Authors:
Ryan B. Hayward;Jeremy P. Spinrad;R. Sritharan
Affiliations:
University of Alberta, Edmonton, Canada;Vanderbilt University, Nashville TN;The University of Dayton, College Park, Dayton OH
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2007

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Abstract

We use a new structural theorem on the presence of two-pairs in weakly chordal graphs to develop improved algorithms. For the recognition problem, we reduce the time complexity from O(mn2) to O(m2) and the space complexity from O(n3) to O(m + n), and also produce a hole or antihole if the input graph is not weakly chordal. For the optimization problems, the complexity of the clique and coloring problems is reduced from O(mn2) to O(n3) and the complexity of the independent set and clique cover problems is improved from O(n4) to O(mn). The space complexity of our optimization algorithms is O(m + n).