0/1/all CSPs, half-integral A-path packing, and linear-time FPT algorithms

Yoichi Iwata, Yutaro Yamaguchi, Yuichi Yoshida

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

A recent trend in the design of FPT algorithms is exploiting the half-integrality of LP relaxations. In other words, starting with a half-integral optimal solution to an LP relaxation, we assign integral values to variables one-by-one by branch and bound. This technique is general and the resulting time complexity has a low dependency on the parameter. However, the time complexity often becomes a large polynomial in the input size because we need to compute half-integral optimal LP solutions. In this paper, we address this issue by providing an O(km)-time algorithm for solving the LPs arising from various FPT problems, where k is the optimal value and m is the number of edges/constraints. Our algorithm is based on interesting connections among 0/1/all constraints, which has been studied in the field of constraints satisfaction, A-path packing, which has been studied in the field of combinatorial optimization, and the LPs used in FPT algorithms. With the aid of this algorithm, we obtain linear-time FPT algorithms for various problems. The obtained running time for each problem is linear in the input size and has the current smallest dependency on the parameter. Most importantly, instead of using problem-specific approaches, we obtain all of these results by a unified approach, i.e., the branch-and-bound framework combined with the efficient computation of half-integral LPs, which demonstrates its generality.

Original languageEnglish
Title of host publicationProceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
EditorsMikkel Thorup
PublisherIEEE Computer Society
Pages462-473
Number of pages12
ISBN (Electronic)9781538642306
DOIs
Publication statusPublished - Nov 30 2018
Externally publishedYes
Event59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 - Paris, France
Duration: Oct 7 2018Oct 9 2018

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2018-October
ISSN (Print)0272-5428

Conference

Conference59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
CountryFrance
CityParis
Period10/7/1810/9/18

All Science Journal Classification (ASJC) codes

  • Computer Science(all)

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  • Cite this

    Iwata, Y., Yamaguchi, Y., & Yoshida, Y. (2018). 0/1/all CSPs, half-integral A-path packing, and linear-time FPT algorithms. In M. Thorup (Ed.), Proceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 (pp. 462-473). [8555129] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2018-October). IEEE Computer Society. https://doi.org/10.1109/FOCS.2018.00051