On the Parameterized Complexity of Reconfiguration Problems

We present the first results on the parameterized complexity of reconfiguration problems, where a reconfiguration variant of an optimization problem Q takes as input two feasible solutions S and T and determines if there is a sequence of reconfiguration steps, i.e. a reconfiguration sequence, that c...

Full description

Saved in:
Bibliographic Details
Published in:Algorithmica Vol. 78; no. 1; pp. 274 - 297
Main Authors: Mouawad, Amer E., Nishimura, Naomi, Raman, Venkatesh, Simjour, Narges, Suzuki, Akira
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2017
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Apexes
Complexity
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Graph theory
Mathematics of Computing
Optimization
Parameterization
Reconfiguration
Theory of Computation
Vertex sets
Vertex cover
Hitting set
Solution space
Parameterized complexity
Reconfiguration
ISSN:0178-4617, 1432-0541
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We present the first results on the parameterized complexity of reconfiguration problems, where a reconfiguration variant of an optimization problem Q takes as input two feasible solutions S and T and determines if there is a sequence of reconfiguration steps, i.e. a reconfiguration sequence, that can be applied to transform S into T such that each step results in a feasible solution to Q . For most of the results in this paper, S and T are sets of vertices of a given graph and a reconfiguration step adds or removes a vertex. Our study is motivated by results establishing that for many NP -hard problems, the classical complexity of reconfiguration is PSPACE -complete. We address the question for several important graph properties under two natural parameterizations: k , a bound on the size of solutions, and ℓ , a bound on the length of reconfiguration sequences. Our first general result is an algorithmic paradigm, the reconfiguration kernel, used to obtain fixed-parameter tractable algorithms for reconfiguration variants of Vertex Cover and, more generally, Bounded Hitting Set and Feedback Vertex Set , all parameterized by k . In contrast, we show that reconfiguring Unbounded Hitting Set is W[2] -hard when parameterized by k + ℓ . We also demonstrate the W[1] -hardness of reconfiguration variants of a large class of maximization problems parameterized by k + ℓ , and of their corresponding deletion problems parameterized by ℓ ; in doing so, we show that there exist problems in FPT when parameterized by k , but whose reconfiguration variants are W[1] -hard when parameterized by k + ℓ .
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-016-0159-2