Parameterized Complexity of Path Set Packing

In Path Set Packing , the input is an undirected graph G , a collection of simple paths in G , and a positive integer k . The problem is to decide whether there exist k edge-disjoint paths in . We study the parameterized complexity of Path Set Packing with respect to both natural and structural para...

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Bibliographic Details
Published in:Algorithmica Vol. 87; no. 12; pp. 1864 - 1898
Main Authors: Aravind, N. R., Saxena, Roopam
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2025
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Combinatorial analysis
Complexity
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Feedback
Mathematics of Computing
Parameterization
Parameters
Theory of Computation
Path set packing
Graph algorithms
Parameterized complexity
Set packing
Fixed parameter tractability
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:In Path Set Packing , the input is an undirected graph G , a collection of simple paths in G , and a positive integer k . The problem is to decide whether there exist k edge-disjoint paths in . We study the parameterized complexity of Path Set Packing with respect to both natural and structural parameters. We show that the problem is W[1]-hard with respect to vertex cover number, and W[1]-hard respect to pathwidth plus solution size when input graph is a grid. These results answer an open question raised in Xu and Zhang (in: Wang L, Zhu D (eds) Computing and combinatorics—24th international conference, COCOON 2018, Qing Dao, China, July 2–4, 2018, proceedings. Lecture notes in computer science, vol 10976, pp 305–315. Springer, 2018, https://doi.org/10.1007/978-3-319-94776-1_26 ). On the positive side, we present an FPT algorithm parameterized by feedback vertex number plus maximum degree, and present an FPT algorithm parameterized by treewidth plus maximum degree plus maximum length of a path in . These positive results complement the hardness of Path Set Packing with respect to any subset of the parameters used in the FPT algorithms. We also give a 4-approximation algorithm for maximum path set packing problem which runs in FPT time when parameterized by feedback edge number.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-025-01329-5