TY - GEN

T1 - Decremental Optimization of Dominating Sets Under the Reconfiguration Framework

AU - Blanché, Alexandre

AU - Mizuta, Haruka

AU - Ouvrard, Paul

AU - Suzuki, Akira

N1 - Funding Information:
Partially supported by JSPS and MAEDI under the Japan-France Integrated Action Program (SAKURA). The first and third author is partially supported by ANR project GrR (ANR-18-CE40-0032). The second author is partially supported by JSPS KAK-ENHI Grant Number JP19J10042, Japan. The third author is partially supported by ANR project GraphEn (ANR-15-CE40-0009). The fourth author is partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP17K12636 and JP18H04091, Japan. Full version available at https://arxiv.org/abs/1906.05163.
Publisher Copyright:
© Springer Nature Switzerland AG 2020.

PY - 2020

Y1 - 2020

N2 - Given a dominating set, how much smaller a dominating set can we find through elementary operations? Here, we proceed by iterative vertex addition and removal while maintaining the property that the set forms a dominating set of bounded size. This can be seen as the optimization variant of the dominating set reconfiguration problem, where two dominating sets are given and the question is merely whether they can be reached from one another through elementary operations. We show that this problem is PSPACE-complete, even if the input graph is a bipartite graph, a split graph, or has bounded pathwidth. On the positive side, we give linear-time algorithms for cographs, trees and interval graphs. We also study the parameterized complexity of this problem. More precisely, we show that the problem is W[2]-hard when parameterized by the upper bound on the size of an intermediary dominating set. On the other hand, we give fixed-parameter algorithms with respect to the minimum size of a vertex cover, or d + s where d is the degeneracy and s is the upper bound of the output solution.

AB - Given a dominating set, how much smaller a dominating set can we find through elementary operations? Here, we proceed by iterative vertex addition and removal while maintaining the property that the set forms a dominating set of bounded size. This can be seen as the optimization variant of the dominating set reconfiguration problem, where two dominating sets are given and the question is merely whether they can be reached from one another through elementary operations. We show that this problem is PSPACE-complete, even if the input graph is a bipartite graph, a split graph, or has bounded pathwidth. On the positive side, we give linear-time algorithms for cographs, trees and interval graphs. We also study the parameterized complexity of this problem. More precisely, we show that the problem is W[2]-hard when parameterized by the upper bound on the size of an intermediary dominating set. On the other hand, we give fixed-parameter algorithms with respect to the minimum size of a vertex cover, or d + s where d is the degeneracy and s is the upper bound of the output solution.

KW - Combinatorial reconfiguration

KW - Dominating set

KW - Parameterized complexity

UR - http://www.scopus.com/inward/record.url?scp=85086222738&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85086222738&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-48966-3_6

DO - 10.1007/978-3-030-48966-3_6

M3 - Conference contribution

AN - SCOPUS:85086222738

SN - 9783030489656

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 69

EP - 82

BT - Combinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings

A2 - Gasieniec, Leszek

A2 - Gasieniec, Leszek

A2 - Klasing, Ralf

A2 - Radzik, Tomasz

PB - Springer

T2 - 31st International Workshop on Combinatorial Algorithms, IWOCA 2020

Y2 - 8 June 2020 through 10 June 2020

ER -