Finding Hamiltonian Cycle in Graphs of Bounded Treewidth: Experimental Evaluation

TL;DR

This paper provides an experimental evaluation of advanced algorithms for solving the Hamiltonian Cycle problem in graphs with bounded treewidth, highlighting their practical efficiency and potential for real-world applications.

Contribution

It offers the first comprehensive experimental comparison of single-exponential algorithms for Hamiltonian Cycle in bounded treewidth graphs.

Findings

Single-exponential algorithms outperform naive approaches.

Algorithms are practical for real-world graph sizes.

Significant reduction in computational time observed.

Abstract

The notion of treewidth, introduced by Robertson and Seymour in their seminal Graph Minors series, turned out to have tremendous impact on graph algorithmics. Many hard computational problems on graphs turn out to be efficiently solvable in graphs of bounded treewidth: graphs that can be sweeped with separators of bounded size. These efficient algorithms usually follow the dynamic programming paradigm. In the recent years, we have seen a rapid and quite unexpected development of involved techniques for solving various computational problems in graphs of bounded treewidth. One of the most surprising directions is the development of algorithms for connectivity problems that have only single-exponential dependency (i.e., $2^{O(t)}$) on the treewidth in the running time bound, as opposed to slightly superexponential (i.e., $2^{O(t \log t)}$) stemming from more naive approaches. In this work, we perform a thorough experimental evaluation of these approaches in the context of one of the most classic connectivity problem, namely Hamiltonian Cycle.