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Reconfiguration Problems

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

Deadline for manuscript submissions: closed (28 February 2018) | Viewed by 30294

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Prof. Dr. Faisal N. Abu-Khzam

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Guest Editor

Department of Computer Science and Mathematics, Lebanese American University, 1102 Beirut, Lebanon
Interests: design and analysis of algorithms; algorithmic graph theory; fixed-parameter algorithms

Prof. Dr. Henning Fernau

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Guest Editor

Informatikwissenschaften, Fachbereich 4, Universität Trier, Universitätsring 15, 54296 Trier, Germany
Interests: complexity theory; fixed parameter algorithms; formal languages; fractal geometry; learning algorithms (machine learning) and pattern recognition
Special Issues, Collections and Topics 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, Collections and Topics 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 submissions that pass pre-check are 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 1600 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.

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Published Papers (5 papers)

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Editorial

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2 pages, 157 KiB

Open AccessEditorial

Special Issue on Reconfiguration Problems

by Faisal Abu-Khzam, Henning Fernau and Ryuhei Uehara

Algorithms 2018, 11(11), 187; https://doi.org/10.3390/a11110187 - 19 Nov 2018

Viewed by 2971

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 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

Jump to: Editorial

15 pages, 316 KiB

Open AccessArticle

Complexity of Hamiltonian Cycle Reconfiguration

by Asahi Takaoka

Algorithms 2018, 11(9), 140; https://doi.org/10.3390/a11090140 - 17 Sep 2018

Cited by 15 | Viewed by 4359

Abstract

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}, \dots, C_{t}

such that

C_{i}

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}, \dots, C_{t}

such that

C_{i}

can be obtained from

C_{i - 1}

by a switch for each i with

1 \leq i \leq 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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25 pages, 524 KiB

Open AccessArticle

Introduction to Reconfiguration

by Naomi Nishimura

Algorithms 2018, 11(4), 52; https://doi.org/10.3390/a11040052 - 19 Apr 2018

Cited by 179 | Viewed by 12232

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, 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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14 pages, 323 KiB

Open AccessFeature PaperArticle

Connectivity and Hamiltonicity of Canonical Colouring Graphs of Bipartite and Complete Multipartite Graphs

by Ruth Haas and Gary MacGillivray

Algorithms 2018, 11(4), 40; https://doi.org/10.3390/a11040040 - 29 Mar 2018

Cited by 3 | Viewed by 4607

Abstract

A k-colouring of a graph G with colours

1, 2, \dots, k

is canonical with respect to an ordering

π = v_{1}, v_{2}, \dots, v_{n}

of the vertices of G if adjacent vertices [...] Read more.

A k-colouring of a graph G with colours

1, 2, \dots, k

is canonical with respect to an ordering

π = v_{1}, v_{2}, \dots, v_{n}

of the vertices of G if adjacent vertices are assigned different colours and, for

1 \leq c \leq 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}

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 \geq 3

. The paper concludes with a detailed consideration of

{Can}_{k}^{π} (K_{2, 2, \dots, 2})

. For each

k \geq χ

and all vertex orderings

π

, it is proved that

{Can}_{k}^{π} (K_{2, 2, \dots, 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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21 pages, 919 KiB

Open AccessArticle

Vertex Cover Reconfiguration and Beyond

by Amer E. Mouawad, Naomi Nishimura, Venkatesh Raman and Sebastian Siebertz

Algorithms 2018, 11(2), 20; https://doi.org/10.3390/a11020020 - 9 Feb 2018

Cited by 16 | Viewed by 4951

Abstract

In the Vertex Cover Reconfiguration (VCR) problem, given a graph G, positive integers k and ℓ 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 ℓ 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 ℓ, 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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