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 -