Optimized 2-Approximation of Treewidth

TL;DR

This paper introduces a linear fixed-parameter tractable algorithm that efficiently computes a tree decomposition with a 2-approximation of treewidth, significantly reducing exponential dependence on the parameter k.

Contribution

It presents a new FPT algorithm with improved exponential dependence for approximating treewidth, enhancing efficiency over previous methods.

Findings

Runs in time $O( ext{poly}(k) 81^k n)$

Reduces exponential base from 1782 to 81

Provides a practical approach for treewidth approximation

Abstract

This paper presents a linear FPT algorithm to find a tree decomposition with a 2-approximation of the treewidth with a significantly smaller exponential dependence on the treewidth. The algorithm runs in time $O(\text{poly}(k) 81^k n)$, compared to Korhonen's running time of $O(\text{poly}(k) 1782^k n)$ = $O(2^{10.8k} n)$.