A Single-Exponential Time 2-Approximation Algorithm for Treewidth

We give an algorithm, that given an n-vertex graph G and an integer k, in time 2 O(k) n either outputs a tree decomposition of G of width at most 2k + 1 or determines that the treewidth of G is larger than k. This is the first 2-approximation algorithm for treewidth that is faster than the known exa...

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Bibliographic Details
Published in:Proceedings / annual Symposium on Foundations of Computer Science pp. 184 - 192
Main Author: Korhonen, Tuukka
Format: Conference Proceeding
Language:English
Published: IEEE 01.02.2022
Subjects:
Approximation algorithms
Computer science
Dynamic programming
FPT-approximation
Heuristic algorithms
Time complexity
treewidth
Upper bound
ISSN:2575-8454
Online Access:Get full text
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Summary:We give an algorithm, that given an n-vertex graph G and an integer k, in time 2 O(k) n either outputs a tree decomposition of G of width at most 2k + 1 or determines that the treewidth of G is larger than k. This is the first 2-approximation algorithm for treewidth that is faster than the known exact algorithms. In particular, our algorithm improves upon both the previous best approximation ratio of 5 in time 2 O(k) n and the previous best approximation ratio of 3 in time 2 O(k) n O(1) , both given by Bodlaender et al. [FOCS 2013, SICOMP 2016]. Our algorithm is based on a local improvement method adapted from a proof of Bellenbaum and Diestel [Comb. Probab. Comput. 2002].
ISSN:2575-8454
DOI:10.1109/FOCS52979.2021.00026