Spanning trees and the complexity of flood-filling games

Meeks, K. and Scott, A. (2014) Spanning trees and the complexity of flood-filling games. Theory of Computing Systems, 54(4), pp. 731-753. (doi:10.1007/s00224-013-9482-z)

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Publisher's URL: http://dx.doi.org/10.1007/s00224-013-9482-z

Abstract

We consider problems related to the combinatorial game (Free-) Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. We show that the minimum number of moves required to flood any given graph G is equal to the minimum, taken over all spanning trees T of G, of the number of moves required to flood T. This result is then applied to give two polynomial-time algorithms for flood-filling problems. Firstly, we can compute in polynomial time the minimum number of moves required to flood a graph with only a polynomial number of connected subgraphs. Secondly, given any coloured connected graph and a subset of the vertices of bounded size, the number of moves required to connect this subset can be computed in polynomial time.

Item Type:Articles
Additional Information:The final publication is available at Springer via http://dx.doi.org/10.1007/s00224-013-9482-z
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Meeks, Dr Kitty
Authors: Meeks, K., and Scott, A.
Subjects:Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Theory of Computing Systems
Publisher:Springer Verlag
ISSN:1432-4350
ISSN (Online):1433-0490
Copyright Holders:Copyright © 2013 Springer Science+Business Media New York
First Published:First published in Theory of Computing Systems 54(4):731-753
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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