Special Issue "Reconfiguration Problems"

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (28 February 2018).

Special Issue Editors

Prof. Dr. Faisal N. Abu-Khzam
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Guest Editor
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
Interests: design and analysis of algorithms; algorithmic graph theory; fixed-parameter algorithms
Prof. Dr. Henning Fernau
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Guest Editor
Theoretical Computer Science, FB 4-Abteilung Informatik, Universität Trier, D-54286 Trier, Germany
Interests: complexity theory; fixed parameter algorithms; formal languages; fractal geometry; learning algorithms (machine learning) and pattern recognition
Special Issues and Collections in MDPI journals
Prof. Dr. Ryuhei Uehara
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Guest Editor
School of Information Science (JAIST), 1-1 Asahidai, Nomi, Ishikawa, 923-1292 Japan
Interests: computational complexity; graph theory; algorithms
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

The topic of reconfiguration problems has featured quite highly in recent workshops and conferences. The basic idea is to consider the scenario of moving from one given (feasible) solution to another, maintaining feasibility for all intermediate solutions. A typical application background would be for a reorganization or repair work that has to be done without interruption to the service that is provided.

The open access journal Algorithms will host a Special Issue on Reconfiguration Problems.

The goal of this Special Issue is to offer a forum for exchanging new ideas about the analysis, design and possibly also implementation of algorithms for reconfiguration problems.

The following is a (non-exhaustive) list of topics of interest:

 Algorithms for reconfiguration of combinatorial graph algorithms

  • Reconfiguration and games
  • Recoloring in graphs
  • Notions of distance and connectivity in solution spaces
  • Computational complexity of reconfiguration
  • Algorithms for reconfiguration of real-world problems
  • Complexity of reconfiguration problems on special graph classes
Dr. Faisal Abu-Khzam
Prof. Dr. Henning Fernau
Prof. Dr. Ryuhei Uehara
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (5 papers)

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Editorial

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Open AccessEditorial
Special Issue on Reconfiguration Problems
Algorithms 2018, 11(11), 187; https://doi.org/10.3390/a11110187 - 19 Nov 2018
Abstract
The study of reconfiguration problems has grown into a field of its own. The basic idea is to consider the scenario of moving from one given (feasible) solution to another, maintaining feasibility for all intermediate solutions. The solution space is often represented by [...] Read more.
The study of reconfiguration problems has grown into a field of its own. The basic idea is to consider the scenario of moving from one given (feasible) solution to another, maintaining feasibility for all intermediate solutions. The solution space is often represented by a “reconfiguration graph”, where vertices represent solutions to the problem in hand and an edge between two vertices means that one can be obtained from the other in one step. A typical application background would be for a reorganization or repair work that has to be done without interruption to the service that is provided. Full article
(This article belongs to the Special Issue Reconfiguration Problems)

Research

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Open AccessArticle
Complexity of Hamiltonian Cycle Reconfiguration
Algorithms 2018, 11(9), 140; https://doi.org/10.3390/a11090140 - 17 Sep 2018
Cited by 2
Abstract
The Hamiltonian cycle reconfiguration problem asks, given two Hamiltonian cycles C0 and Ct of a graph G, whether there is a sequence of Hamiltonian cycles C0,C1,,Ct such that Ci can [...] Read more.
The Hamiltonian cycle reconfiguration problem asks, given two Hamiltonian cycles C 0 and C t of a graph G, whether there is a sequence of Hamiltonian cycles C 0 , C 1 , , C t such that C i can be obtained from C i 1 by a switch for each i with 1 i t , where a switch is the replacement of a pair of edges u v and w z on a Hamiltonian cycle with the edges u w and v z of G, given that u w and v z did not appear on the cycle. We show that the Hamiltonian cycle reconfiguration problem is PSPACE-complete, settling an open question posed by Ito et al. (2011) and van den Heuvel (2013). More precisely, we show that the Hamiltonian cycle reconfiguration problem is PSPACE-complete for chordal bipartite graphs, strongly chordal split graphs, and bipartite graphs with maximum degree 6. Bipartite permutation graphs form a proper subclass of chordal bipartite graphs, and unit interval graphs form a proper subclass of strongly chordal graphs. On the positive side, we show that, for any two Hamiltonian cycles of a bipartite permutation graph and a unit interval graph, there is a sequence of switches transforming one cycle to the other, and such a sequence can be obtained in linear time. Full article
(This article belongs to the Special Issue Reconfiguration Problems)
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Open AccessArticle
Introduction to Reconfiguration
Algorithms 2018, 11(4), 52; https://doi.org/10.3390/a11040052 - 19 Apr 2018
Cited by 24
Abstract
Reconfiguration is concerned with relationships among solutions to a problem instance, where the reconfiguration of one solution to another is a sequence of steps such that each step produces an intermediate feasible solution. The solution space can be represented as a reconfiguration graph [...] Read more.
Reconfiguration is concerned with relationships among solutions to a problem instance, where the reconfiguration of one solution to another is a sequence of steps such that each step produces an intermediate feasible solution. The solution space can be represented as a reconfiguration graph, where two vertices representing solutions are adjacent if one can be formed from the other in a single step. Work in the area encompasses both structural questions (Is the reconfiguration graph connected?) and algorithmic ones (How can one find the shortest sequence of steps between two solutions?) This survey discusses techniques, results, and future directions in the area. Full article
(This article belongs to the Special Issue Reconfiguration Problems)
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Open AccessFeature PaperArticle
Connectivity and Hamiltonicity of Canonical Colouring Graphs of Bipartite and Complete Multipartite Graphs
Algorithms 2018, 11(4), 40; https://doi.org/10.3390/a11040040 - 29 Mar 2018
Cited by 2
Abstract
A k-colouring of a graph G with colours 1,2,,k is canonical with respect to an ordering π=v1,v2,,vn of the vertices of G if adjacent vertices [...] Read more.
A k-colouring of a graph G with colours 1 , 2 , , k is canonical with respect to an ordering π = v 1 , v 2 , , v n of the vertices of G if adjacent vertices are assigned different colours and, for 1 c k , whenever colour c is assigned to a vertex v i , each colour less than c has been assigned to a vertex that precedes v i in π . The canonical k-colouring graph of G with respect to π is the graph Can k π ( G ) with vertex set equal to the set of canonical k-colourings of G with respect to π , with two of these being adjacent if and only if they differ in the colour assigned to exactly one vertex. Connectivity and Hamiltonicity of canonical colouring graphs of bipartite and complete multipartite graphs is studied. It is shown that for complete multipartite graphs, and bipartite graphs there exists a vertex ordering π such that Can k π ( G ) is connected for large enough values of k. It is proved that a canonical colouring graph of a complete multipartite graph usually does not have a Hamilton cycle, and that there exists a vertex ordering π such that Can k π ( K m , n ) has a Hamilton path for all k 3 . The paper concludes with a detailed consideration of Can k π ( K 2 , 2 , , 2 ) . For each k χ and all vertex orderings π , it is proved that Can k π ( K 2 , 2 , , 2 ) is either disconnected or isomorphic to a particular tree. Full article
(This article belongs to the Special Issue Reconfiguration Problems)
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Open AccessArticle
Vertex Cover Reconfiguration and Beyond
Algorithms 2018, 11(2), 20; https://doi.org/10.3390/a11020020 - 09 Feb 2018
Cited by 3
Abstract
In the Vertex Cover Reconfiguration (VCR) problem, given a graph G, positive integers k and and two vertex covers S and T of G of size at most k, we determine whether S can be transformed into T by a [...] Read more.
In the Vertex Cover Reconfiguration (VCR) problem, given a graph G, positive integers k and and two vertex covers S and T of G of size at most k, we determine whether S can be transformed into T by a sequence of at most vertex additions or removals such that every operation results in a vertex cover of size at most k. Motivated by results establishing the W [ 1 ] -hardness of VCR when parameterized by , we delineate the complexity of the problem restricted to various graph classes. In particular, we show that VCR remains W [ 1 ] -hard on bipartite graphs, is NP -hard, but fixed-parameter tractable on (regular) graphs of bounded degree and more generally on nowhere dense graphs and is solvable in polynomial time on trees and (with some additional restrictions) on cactus graphs. Full article
(This article belongs to the Special Issue Reconfiguration Problems)
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