Spanning Trees and the Complexity of Flood-Filling Games

Meeks, K. and Scott, A. (2012) Spanning Trees and the Complexity of Flood-Filling Games. In: Sixth International Conference on Fun with Algorithms (FUN 2012), Venice, Italy, 04-06 Jun 2012, pp. 282-292. ISBN 9783642303463 (doi: 10.1007/978-3-642-30347-0_28)

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: Conference Proceedings
• 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
• ISSN: 0302-9743
• ISBN: 9783642303463
• Copyright Holders: Copyright © 2012 Springer-Verlag Berlin Heidelberg
• First Published: First published in Fun with Algorithms: 282-292
• Publisher Policy: Reproduced in accordance with the publisher copyright policy