Efficient Approximation for Triangulation of Minimum Treewidth

Abstract: We present four novel approximation algorithms for finding triangulation of minimum treewidth. Two of the algorithms improve on the running times of algorithms by Robertson and Seymour, and Becker and Geiger that approximate the optimum by factors of 4 and 3 2/3, respectively. A third algorithm is faster than those but gives an approximation factor of 4 1/2. The last algorithm is yet faster, producing factor-O(lg/k) approximations in polynomial time. Finding triangulations of minimum treewidth for graphs is central to many problems in computer science. Real-world problems in artificial intelligence, VLSI design and databases are efficiently solvable if we have an efficient approximation algorithm for them. We report on experimental results confirming the effectiveness of our algorithms for large graphs associated with real-world problems.