Parameterized Complexity of (A,l)-Path Packing

Rémy Belmonte, Tesshu Hanaka, Masaaki Kanzaki, Masashi Kiyomi, Yasuaki Kobayashi, Yusuke Kobayashi, Michael Lampis, Hirotaka Ono, Yota Otachi

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

1 Citation (Scopus)


Given a graph G = (V, E), (Formula Presented), and integers k and ℓ, the (A, ℓ)-Path Packing problem asks to find k vertex-disjoint paths of length ℓ that have endpoints in A and internal points in V \ A. We study the parameterized complexity of this problem with parameters |A|, ℓ, k, treewidth, pathwidth, and their combinations. We present sharp complexity contrasts with respect to these parameters. Among other results, we show that the problem is polynomial-time solvable when ℓ ≤ 3, while it is NP-complete for constant ℓ ≥ 4. We also show that the problem is W[1]-hard parameterized by pathwidth+|A|, while it is fixed-parameter tractable parameterized by treewidth + ℓ.

Original languageEnglish
Title of host publicationCombinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings
EditorsLeszek Gasieniec, Leszek Gasieniec, Ralf Klasing, Tomasz Radzik
Number of pages13
ISBN (Print)9783030489656
Publication statusPublished - 2020
Externally publishedYes
Event31st International Workshop on Combinatorial Algorithms, IWOCA 2020 - Bordeaux, France
Duration: Jun 8 2020Jun 10 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12126 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference31st International Workshop on Combinatorial Algorithms, IWOCA 2020

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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