Efficient Approximation for Triangulation of Minimum Treewidth

TL;DR

This paper introduces four new approximation algorithms for finding graph triangulations with near-minimum treewidth, improving efficiency and approximation factors, and demonstrates their effectiveness on large real-world graphs.

Contribution

The paper presents four novel approximation algorithms for minimum treewidth triangulation, with improved running times and approximation factors over previous methods.

Findings

Algorithms outperform previous methods in speed and accuracy.

Effective on large, real-world graphs.

Approximation factors range from 4 to logarithmic.

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.