In the minimum fill-in problem, one wishes to find a set of edges of smallest size, whose addition to a given graph will make it chordal. The problem has important applications in numerical algebra and has been studied intensively since the 1970s. We give the first polynomial approximation algorithm for the problem. Our algorithm constructs a triangulation whose size is at most eight times the optimum size squared. The algorithm builds on the recent parameterized algorithm of Kaplan, Shamir and Tarjan for the same problem. For bounded degree graphs we give a polynomial approximation algorithm with a polylogarithmic approximation ratio. We also improve the parameterized algorithm.
|Number of pages
|Conference Proceedings of the Annual ACM Symposium on Theory of Computing
|Published - 1998
|Proceedings of the 1998 30th Annual ACM Symposium on Theory of Computing - Dallas, TX, USA
Duration: 23 May 1998 → 26 May 1998