Parameterized algorithms and data reduction for the short secluded s‐t‐path problem

• Published in: Networks Vol. 75; no. 1; pp. 34 - 63
• Main Authors: Bevern, René, Fluschnik, Till, Tsidulko, Oxana Yu
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.01.2020; Wiley Subscription Services, Inc
• Subjects: Algorithms; Apexes; Data reduction; Feedback; fixed‐parameter tractability; Graph theory; kernelization lower bounds; NP‐hard problem; Parameterization; Parameters; Polynomials; problem kernelization; subexponential time; treewidth
• ISSN: 0028-3045; 1097-0037
• DOI: 10.1002/net.21904

Given a graph G = (V, E), two vertices s, t ∈ V, and two integers k, ℓ, the Short Secluded Path problem is to find a simple s‐t‐path with at most k vertices and ℓ neighbors. We study the parameterized complexity of the problem with respect to four structural graph parameters: the vertex cover number, treewidth, feedback vertex number, and feedback edge number. In particular, we completely settle the question of the existence of problem kernels with size polynomial in these parameters and their combinations with k and ℓ. We also obtain a 2O(tw) · ℓ2 · n‐time algorithm for n‐vertex graphs of treewidth tw, which yields subexponential‐time algorithms in several graph classes.