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

Yoichi Iwata, Yutaro Yamaguchi, Yuichi Yoshida

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

5 被引用数 (Scopus)

抄録

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.

本文言語英語
ホスト出版物のタイトルProceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
編集者Mikkel Thorup
出版社IEEE Computer Society
ページ462-473
ページ数12
ISBN(電子版)9781538642306
DOI
出版ステータス出版済み - 11 30 2018
外部発表はい
イベント59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 - Paris, フランス
継続期間: 10 7 201810 9 2018

出版物シリーズ

名前Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
2018-October
ISSN(印刷版)0272-5428

会議

会議59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
Countryフランス
CityParis
Period10/7/1810/9/18

All Science Journal Classification (ASJC) codes

  • Computer Science(all)

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