A survey on the parameterized complexity of the independent set and (connected) dominating set reconfiguration problems

Bousquet, Nicolás; Mouawad, Amer E.; Nishimura, Nobuya; Siebertz, Sebastian

doi:10.48550/arxiv.2204.10526

Cited by 2 publications

(3 citation statements)

References 39 publications

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“…On the positive side, polynomial-time algorithms are known only for very simple graph classes such as trees [15]. More positive results (which vary depending on the model) are possible if we consider the parameterized complexity of the problem [9].…”

Section: Related Workmentioning

confidence: 99%

On Solution Discovery via Reconfiguration

Fellows,

Grobler,

Megow

et al. 2023

Frontiers in Artificial Intelligence and Applications

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The dynamics of real-world applications and systems require efficient methods for improving infeasible solutions or restoring corrupted ones by making modifications to the current state of a system in a restricted way. We propose a new framework of solution discovery via reconfiguration for constructing a feasible solution for a given problem by executing a sequence of small modifications starting from a given state. Our framework integrates different aspects of classical local search, reoptimization, and combinatorial reconfiguration. We exemplify our framework on a multitude of fundamental combinatorial problems, namely VERTEX COVER, INDEPENDENT SET, DOMINATING SET, and COLORING. We study the classical as well as the parameterized complexity of the solution discovery variants of those problems and explore the boundary between tractable and intractable instances.

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Section: Related Workmentioning

confidence: 99%

On Solution Discovery via Reconfiguration

Fellows,

Grobler,

Megow

et al. 2023

Frontiers in Artificial Intelligence and Applications

View full text Add to dashboard Cite

show abstract

“…In other words, the combinatorial explosion can be restricted to the parameter k. In the rest A. Agrawal, S. Hait, and A. E. Mouawad 39:3 of the paper, we mainly consider parameters k (the number of tokens) and ℓ (the number of reconfiguration steps). TSO and TJO are known to be W [1]-hard (and XNL-complete [4]) parameterized by k + ℓ on general graphs [8]. TSR and TJR are known to be W [1]-hard (and XL-complete [4]) parameterized by k on general graphs [24] .…”

Section: Introductionmentioning

confidence: 99%

“…Finally, for TSR, the problem becomes fixed-parameter tractable parameterized by k on planar graphs, chordal graphs of bounded clique number, and graphs of bounded degree [2]. We refer the reader to the recent survey by Bousquet et al [8] for more background on the parameterized complexity of these problems.…”

Section: Introductionmentioning

confidence: 99%