Making Life More Confusing for Firefighters

Hand, S. D., Enright, J. and Meeks, K. (2022) Making Life More Confusing for Firefighters. In: 11th International Conference on Fun with Algorithms (FUN 2022), Sicily, Italy, 30 May - 03 Jun 2022, ISBN 9783959772327 (doi: 10.4230/LIPIcs.FUN.2022.15)

Abstract

It is well known that fighting a fire is a hard task. The Firefighter problem asks how to optimally deploy firefighters to defend the vertices of a graph from a fire. This problem is NP-Complete on all but a few classes of graphs. Thankfully, firefighters do not have to work alone, and are often aided by the efforts of good natured civillians who slow the spread of a fire by maintaining firebreaks when they are able. We will show that this help, although well-intentioned, unfortunately makes the optimal deployment of firefighters an even harder problem. To model this scenario we introduce the Temporal Firefighter problem, an extension of Firefighter to temporal graphs. We show that Temporal Firefighter is also NP-Complete, and remains so on all but one of the underlying classes of graphs on which Firefighter is known to have polynomial time solutions. This motivates us to explore making use of the temporal structure of the graph in our search for tractability, and we conclude by presenting an FPT algorithm for Temporal Firefighter with respect to the temporal graph parameter vertex-interval-membership-width.

• Item Type: Conference Proceedings
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Meeks, Dr Kitty and Hand, Samuel and Enright, Dr Jessica
• Authors: Hand, S. D., Enright, J., and Meeks, K.
• College/School: College of Science and Engineering > School of Computing Science
• ISSN: 1868-8969
• ISBN: 9783959772327
• Copyright Holders: Copyright © Samuel D. Hand, Jessica Enright, and Kitty Meeks 2022
• Publisher Policy: Reproduced under a Creative Commons licence

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Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
305944		Multilayer Algorithmics to Leverage Graph Structure	Kitty Meeks	Engineering and Physical Sciences Research Council (EPSRC)	EP/T004878/1	M&S - Statistics
305944		Multilayer Algorithmics to Leverage Graph Structure	Kitty Meeks	Engineering and Physical Sciences Research Council (EPSRC)	EP/T004878/1	M&S - Statistics