The complexity of FREE-FLOOD-IT on 2xn boards

Meeks, K. and Scott, A. (2013) The complexity of FREE-FLOOD-IT on 2xn boards. Theoretical Computer Science, 500, pp. 25-43. (doi: 10.1016/j.tcs.2013.06.010)

Abstract

We consider the complexity of 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. Our main result is that computing the length of an optimal sequence is fixed parameter tractable (with the number of colours as a parameter) when restricted to rectangular 2×n boards. We also show that, when the number of colours is unbounded, the problem remains NP-hard on such boards. These results resolve a question of Clifford, Jalsenius, Montanaro and Sach.

• Item Type: Articles
• Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Theoretical Computer Science, [500, (25 June 2013)] DOI 10.1016/j.tcs.2013.06.010
• 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: Theoretical Computer Science
• Publisher: Elsevier
• ISSN: 0304-3975
• Copyright Holders: Copyright © 2013 Elsevier B.V.
• First Published: First published in Theoretical Computer Science 500:25-43
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher