Using contracted solution graphs for solving reconfiguration problems

Bonsma, P.; Paulusma, D.

doi:10.1007/s00236-019-00336-8

Using contracted solution graphs for solving reconfiguration problems

Bonsma, P.; Paulusma, D.

Authors

P. Bonsma

Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor

Abstract

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 (Discrete Appl Math 231:95–112, 2017) and Hatanaka et al. (IEICE Trans Fundam Electron Commun Comput Sci 98(6):1168–1178, 2015). 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.

Citation

Bonsma, P., & Paulusma, D. (2019). Using contracted solution graphs for solving reconfiguration problems. Acta Informatica, 56(7-8), 619-648. https://doi.org/10.1007/s00236-019-00336-8

Journal Article Type	Article
Acceptance Date	May 20, 2019
Online Publication Date	May 31, 2019
Publication Date	Nov 30, 2019
Deposit Date	May 20, 2019
Publicly Available Date	May 31, 2020
Journal	Acta Informatica
Print ISSN	0001-5903
Electronic ISSN	1432-0525
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	56
Issue	7-8
Pages	619-648
DOI	https://doi.org/10.1007/s00236-019-00336-8
Public URL	https://durham-repository.worktribe.com/output/1296058

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Copyright Statement
This is a post-peer-review, pre-copyedit version of an article published in Acta informatica. The final authenticated version is available online at: https://doi.org/10.1007/s00236-019-00336-8