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: Contribution to journalArticlepeer-review


Given a graph G= (V, E) , A⊆ V, and integers k and ℓ, the (A, ℓ) -Path Packing problem asks to find k vertex-disjoint paths of length exactly 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. Additionally, we study a variant called Short A-Path Packing that asks to find k vertex-disjoint paths of length at mostℓ. We show that all our positive results on the exact-length version can be translated to this version and show the hardness of the cases where |A| or ℓ is a constant.

Original languageEnglish
Pages (from-to)871-895
Number of pages25
Issue number4
Publication statusPublished - Apr 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics


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