{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,12]],"date-time":"2024-03-12T18:43:43Z","timestamp":1710269023161},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2019,2]]},"abstract":" Suppose that a circular fire spreads in the plane at unit speed. A single fire fighter can build a barrier at speed [Formula: see text]. How large must [Formula: see text] be to ensure that the fire can be contained, and how should the fire fighter proceed? We contribute two results. <\/jats:p> First, we analyze the natural curve [Formula: see text] that develops when the fighter keeps building, at speed [Formula: see text], a barrier along the boundary of the expanding fire. We prove that the behavior of this spiralling curve is governed by a complex function [Formula: see text], where [Formula: see text] and [Formula: see text] are real functions of [Formula: see text]. For [Formula: see text] all zeroes are complex conjugate pairs. If [Formula: see text] denotes the complex argument of the conjugate pair nearest to the origin then, by residue calculus, the fire fighter needs [Formula: see text] rounds before the fire is contained. As [Formula: see text] decreases towards [Formula: see text] these two zeroes merge into a real one, so that argument [Formula: see text] goes to 0. Thus, curve [Formula: see text] does not contain the fire if the fighter moves at speed [Formula: see text]. (That speed [Formula: see text] is sufficient for containing the fire has been proposed before by Bressan et al. [6], who constructed a sequence of logarithmic spiral segments that stay strictly away from the fire.) <\/jats:p> Second, we show that for any curve that visits the four coordinate half-axes in cyclic order, and in increasing distances from the origin the fire can not be contained if the speed [Formula: see text] is less than 1.618\u2026, the golden ratio. <\/jats:p>","DOI":"10.1142\/s0129054119500023","type":"journal-article","created":{"date-parts":[[2019,3,13]],"date-time":"2019-03-13T03:51:51Z","timestamp":1552449111000},"page":"231-246","source":"Crossref","is-referenced-by-count":7,"title":["On a Fire Fighter\u2019s Problem"],"prefix":"10.1142","volume":"30","author":[{"given":"Rolf","family":"Klein","sequence":"first","affiliation":[{"name":"Department of Computer Science I, University of Bonn, Friedrich-Ebert-Allee 144, 53113 Bonn, Germany"}]},{"given":"Elmar","family":"Langetepe","sequence":"additional","affiliation":[{"name":"Department of Computer Science I, University of Bonn, Friedrich-Ebert-Allee 144, 53113 Bonn, Germany"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-9535-9950","authenticated-orcid":false,"given":"Barbara","family":"Schwarzwald","sequence":"additional","affiliation":[{"name":"Department of Computer Science I, University of Bonn, Friedrich-Ebert-Allee 144, 53113 Bonn, Germany"}]},{"given":"Christos","family":"Levcopoulos","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Lund University, Box 118, 221 00 Lund, Sweden"}]},{"given":"Andrzej","family":"Lingas","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Lund University, Box 118, 221 00 Lund, Sweden"}]}],"member":"219","published-online":{"date-parts":[[2019,3,12]]},"reference":[{"key":"S0129054119500023BIB002","doi-asserted-by":"publisher","DOI":"10.3390\/a2031069"},{"key":"S0129054119500023BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2007.03.009"},{"key":"S0129054119500023BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-5389-5_2"},{"key":"S0129054119500023BIB006","doi-asserted-by":"publisher","DOI":"10.1142\/S0219530508001146"},{"key":"S0129054119500023BIB007","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20271"},{"key":"S0129054119500023BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.02.039"},{"key":"S0129054119500023BIB009","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2009033"},{"key":"S0129054119500023BIB010","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2010053"},{"key":"S0129054119500023BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-011-0453-4"},{"key":"S0129054119500023BIB012","author":"Falbo C.","year":"1995","journal-title":"Joint Meeting of the Northern and Southern California Sections of the MAA"},{"key":"S0129054119500023BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2005.12.053"},{"issue":"57","key":"S0129054119500023BIB014","first-page":"6","volume":"43","author":"Finbow S.","year":"2009","journal-title":"Australasian Journal of Combinatorics"},{"key":"S0129054119500023BIB015","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801655"},{"key":"S0129054119500023BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-68405-3_7"},{"key":"S0129054119500023BIB023","first-page":"19","volume":"41","author":"Wang P.","year":"2002","journal-title":"Journal of Combinatorial Mathematics and Combinatorial Computing"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054119500023","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:40:17Z","timestamp":1565120417000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054119500023"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2]]},"references-count":15,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2019,3,12]]},"published-print":{"date-parts":[[2019,2]]}},"alternative-id":["10.1142\/S0129054119500023"],"URL":"http:\/\/dx.doi.org\/10.1142\/s0129054119500023","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2]]}}}