TY - JOUR

T1 - Minimum separator reconfiguration

AU - C.M. Gomes, Guilherme

AU - Legrand-Duchesne, Clément

AU - Mahmoud, Reem

AU - Mouawad, Amer E.

AU - Okamoto, Yoshio

AU - F. dos Santos, Vinicius

AU - van der Zanden, Tom C.

N1 - No data was used for the research described in the article.

PY - 2024/12/1

Y1 - 2024/12/1

N2 - We study the problem of reconfiguring s-t-separators on finite simple graphs. We consider several variants of the problem, focusing on the token sliding and jumping models. We begin with a polynomial-time algorithm that computes (if one exists) a shortest sequence of slides and another that decides if a sequence of jumps exists and outputs a witnessing sequence. We also show that deciding if a reconfiguration sequence of at most ℓ jumps exists is an NP-complete problem. To complement this result, we investigate the parameterized complexity of the natural parameterizations of the problem: by the size k of the minimum s-t-separators and by the number of jumps ℓ. We show that the problem is in FPT parameterized by k, but that it does not admit a polynomial kernel unless NP⊆coNP/poly. Our final result is a kernel with O(ℓ
2) vertices and edges.

AB - We study the problem of reconfiguring s-t-separators on finite simple graphs. We consider several variants of the problem, focusing on the token sliding and jumping models. We begin with a polynomial-time algorithm that computes (if one exists) a shortest sequence of slides and another that decides if a sequence of jumps exists and outputs a witnessing sequence. We also show that deciding if a reconfiguration sequence of at most ℓ jumps exists is an NP-complete problem. To complement this result, we investigate the parameterized complexity of the natural parameterizations of the problem: by the size k of the minimum s-t-separators and by the number of jumps ℓ. We show that the problem is in FPT parameterized by k, but that it does not admit a polynomial kernel unless NP⊆coNP/poly. Our final result is a kernel with O(ℓ
2) vertices and edges.

KW - Combinatorial reconfiguration

KW - Kernelization

KW - Minimum separators

KW - Parameterized complexity

U2 - 10.1016/j.jcss.2024.103574

DO - 10.1016/j.jcss.2024.103574

M3 - Article

SN - 0022-0000

VL - 146

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

M1 - 103574

ER -