TY - GEN

T1 - Parameterized Complexity of (A,l)-Path Packing

AU - Belmonte, Rémy

AU - Hanaka, Tesshu

AU - Kanzaki, Masaaki

AU - Kiyomi, Masashi

AU - Kobayashi, Yasuaki

AU - Kobayashi, Yusuke

AU - Lampis, Michael

AU - Ono, Hirotaka

AU - Otachi, Yota

N1 - Funding Information:
Partially supported by PRC CNRS JSPS project PARAGA, by JSPS KAKENHI Grant Numbers JP16K16010, JP17H01698, JP17H01788, JP18H05291, JP18K11157, JP18K11168, JP18K11169, JP18H04091, JP19K21537, and by JST CREST JPMJCR 1401. The authors thank Tatsuya Gima for helpful discussions.
Publisher Copyright:
© Springer Nature Switzerland AG 2020.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85086266613&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85086266613&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-48966-3_4

DO - 10.1007/978-3-030-48966-3_4

M3 - Conference contribution

AN - SCOPUS:85086266613

SN - 9783030489656

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 43

EP - 55

BT - Combinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings

A2 - Gasieniec, Leszek

A2 - Gasieniec, Leszek

A2 - Klasing, Ralf

A2 - Radzik, Tomasz

PB - Springer

T2 - 31st International Workshop on Combinatorial Algorithms, IWOCA 2020

Y2 - 8 June 2020 through 10 June 2020

ER -