The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs

Hatanaka, Tatsuhiko; Ito, Takehiro; Zhou, Xiao

doi:10.1007/978-3-319-12691-3_24

Cited by 4 publications

(16 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[Ours] [4] [ 14] k (no parameter) Bonsma et al [4] and Johnson et al [17] independently developed a fixedparameter algorithm to solve coloring reconfiguration when parameterized by k + ℓ, where ℓ is the upper bound on the length of reconfiguration sequences, and again their algorithms can be applied to list coloring reconfiguration. In contrast, if coloring reconfiguration is parameterized only by ℓ, then it is W[1]-hard when k is an input [4] and does not admit a polynomial kernelization when k is fixed unless the polynomial hierarchy collapses [17].…”

Section: Known and Related Resultsmentioning

confidence: 99%

“…Hatanaka et al [14] proved that list coloring reconfiguration is PSPACE-complete even for complete split graphs, whose modular-width is zero. Wrochna [20] proved that list coloring reconfiguration is PSPACEcomplete even when k and the bandwidth of an input graph are bounded by some constant; thus the treewidth and the cliquewidth of an input graph are also bounded.…”

Section: Known and Related Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Parameterized complexity of the list coloring reconfiguration problem with graph parameters

Hatanaka

Ito

Zhou

2018

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

Let G be a graph such that each vertex has its list of available colors, and assume that each list is a subset of the common set consisting of k colors. For two given list colorings of G, we study the problem of transforming one into the other by changing only one vertex color assignment at a time, while at all times maintaining a list coloring. This problem is known to be PSPACE-complete even for bounded bandwidth graphs and a fixed constant k. In this paper, we study the fixed-parameter tractability of the problem when parameterized by several graph parameters. We first give a fixed-parameter algorithm for the problem when parameterized by k and the modular-width of an input graph. We next give a fixed-parameter algorithm for the shortest variant when parameterized by k and the size of a minimum vertex cover of an input graph. As corollaries, we show that the problem for cographs and the shortest variant for split graphs are fixed-parameter tractable even when only k is taken as a parameter. On the other hand, we prove that the problem is W[1]-hard when parameterized only by the size of a minimum vertex cover of an input graph.Recently, the framework of reconfiguration [16] has been extensively studied in the field of theoretical computer science. This framework models several situations where we wish to find a step-by-step transformation between two feasible solutions of a combinatorial (search) problem such that all intermediate solutions are also feasible and each step respects a fixed reconfiguration rule. This reconfiguration framework has been applied to several well-studied combinatorial problems. (See a survey [15].) Our problemIn this paper, we study a reconfiguration problem for list (vertex) colorings in a graph, which was introduced by Bonsma and Cereceda [2].

show abstract

Section: Known and Related Resultsmentioning

confidence: 99%

Section: Known and Related Resultsmentioning

confidence: 99%

Parameterized complexity of the list coloring reconfiguration problem with graph parameters

Hatanaka

Ito

Zhou

2018

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…Due to the PSPACEcompleteness of S-Reachability, such an algorithm does not terminate in polynomial time for all instances. Hence we aim to identify restricted instance classes for which we do obtain a polynomial running time, as illustrated by a new application explained in Section 1.2 and two known examples [7,20] explained below.…”

Section: Aims and Methodologymentioning

confidence: 99%

“…Bonsma [7] introduced the DP method based on contracted solution graphs to obtain an efficient algorithm for Shortest-Path-Reachability restricted to planar graphs. Hatanaka, Ito and Zhou [20] used this DP method for proving that List-Coloring-Reachability is polynomial-time solvable for caterpillars (in both papers, contracted solution graphs are called encodings). To be more precise, in [20] dynamic programming was done over a path decomposition of the given caterpillar.…”

Section: Aims and Methodologymentioning

confidence: 99%

“…In Section 4 we illustrate our method by giving dynamic programming rules for the C k -Reachability problem that can be used if a tree decomposition of the graph is given. Recall that similar dynamic programming rules have been for other reconfiguration problems [7,20] when a path decomposition is given. Our rules solve the C k -Reachability problem cor-rectly for every graph G and can also be used directly for List-Coloring-Reachability and thus generalize the rules of [20].…”

Section: Aims and Methodologymentioning

confidence: 99%

See 1 more Smart Citation

Using contracted solution graphs for solving reconfiguration problems

Bonsma

Paulusma

2019

Acta Informatica

View full text Add to dashboard Cite

We introduce in a general setting a dynamic programming method for solving reconfiguration problems. Our method is based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge contractions that decrease the graph size without losing any critical information needed to solve the reconfiguration problem under consideration. Our general framework captures the approach behind known reconfiguration results of Bonsma (2012) and Hatanaka, Ito and Zhou (2014). As a third example, we apply the method to the following well-studied problem: given two k-colorings α and β of a graph G, can α be modified into β by recoloring one vertex of G at a time, while maintaining a k-coloring throughout? This problem is known to be PSPACE-hard even for bipartite planar graphs and k = 4. By applying our method in combination with a thorough exploitation of the graph structure we obtain a polynomial-time algorithm for (k − 2)-connected chordal graphs.

show abstract

Reconfiguration of maximum-weight b-matchings in a graph

et al. 2018

Self Cite

View full text Add to dashboard Cite

Consider a graph such that each vertex has a nonnegative integer capacity and each edge has a positive integer weight. Then, a b-matching in the graph is a multi-set of edges (represented by an integer vector on edges) such that the total number of edges incident to each vertex is at most the capacity of the vertex. In this paper, we study a reconfiguration variant for maximum-weight b-matchings: For two given maximum-weight b-matchings in a graph, we are asked to determine whether there exists a sequence of maximum-weight b-matchings in the graph between them, with subsequent b-matchings obtained by removing one edge and adding another. We show that this reconfiguration problem is solvable in polynomial time for instances with no integrality gap. Such instances include bipartite graphs with any capacity function on vertices, and 2-matchings in general graphs. Thus, our result implies that the reconfiguration problem for maximum-weight matchings can be solved in polynomial time for bipartite graphs.

show abstract

The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs

Cited by 4 publications

References 29 publications

Parameterized complexity of the list coloring reconfiguration problem with graph parameters

Parameterized complexity of the list coloring reconfiguration problem with graph parameters

Using contracted solution graphs for solving reconfiguration problems

Reconfiguration of maximum-weight b-matchings in a graph

Contact Info

Product

Resources

About