Minimum Separator Reconfiguration
Guilherme C. M. Gomes, Cl\'ement Legrand-Duchesne, Reem Mahmoud, and Amer E. Mouawad, Yoshio Okamoto, Vinicius F. dos Santos, Tom C., van der Zanden

TL;DR
This paper investigates reconfiguring minimum s-t separators in graphs, providing polynomial algorithms for some variants, proving NP-completeness for others, and exploring fixed-parameter tractability and kernelization results.
Contribution
It introduces polynomial-time algorithms for reconfiguring minimum s-t separators via slides and jumps, and analyzes the complexity and parameterized aspects of jump sequences.
Findings
Polynomial-time algorithm for minimum-length slide sequences.
Decidability of jump sequences in polynomial time.
NP-completeness of bounded jump sequence problem.
Abstract
We study the problem of reconfiguring one minimum --separator into another minimum --separator in some -vertex graph containing two non-adjacent vertices and . We consider several variants of the problem as we focus on both the token sliding and token jumping models. Our first contribution is a polynomial-time algorithm that computes (if one exists) a minimum-length sequence of slides transforming into . We additionally establish that the existence of a sequence of jumps (which need not be of minimum length) can be decided in polynomial time (by an algorithm that also outputs a witnessing sequence when one exists). In contrast, and somewhat surprisingly, we show that deciding if a sequence of at most jumps can transform into is an -complete problem. To complement this negative result, we investigate the parameterized…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
