About: Fast exact algorithm for L(2,1)-labeling of graphs

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1016/j.tcs.2012.06.037
Description	An L(2, 1)-labeling of a graph is a mapping from its vertex set into nonnegative integers such that the labels assigned to adjacent vertices differ by at least 2, and labels assigned to vertices of distance 2 are different. The span of such a labeling is the maximum label used, and the L(2, 1)-span of a graph is the minimum possible span of its L(2, 1)-labelings. We show how to compute the L(2, 1)-span of a connected graph in time O(2.6488(n)). Previously published exact exponential time algorithms were gradually improving the base of the exponential function from 4 to the so far best known 3, with 3 itself seemingly having been the Holy Grail for quite a while. As concerns special graph classes, we are able to solve the problem in time O(2.5944(n)) for claw-free graphs, and in time O(2(n-r)(2 + n/r)(r)) for graphs having a dominating set of size r. An L(2, 1)-labeling of a graph is a mapping from its vertex set into nonnegative integers such that the labels assigned to adjacent vertices differ by at least 2, and labels assigned to vertices of distance 2 are different. The span of such a labeling is the maximum label used, and the L(2, 1)-span of a graph is the minimum possible span of its L(2, 1)-labelings. We show how to compute the L(2, 1)-span of a connected graph in time O(2.6488(n)). Previously published exact exponential time algorithms were gradually improving the base of the exponential function from 4 to the so far best known 3, with 3 itself seemingly having been the Holy Grail for quite a while. As concerns special graph classes, we are able to solve the problem in time O(2.5944(n)) for claw-free graphs, and in time O(2(n-r)(2 + n/r)(r)) for graphs having a dominating set of size r. (en)
Title	Fast exact algorithm for L(2,1)-labeling of graphs Fast exact algorithm for L(2,1)-labeling of graphs (en)
skos:prefLabel	Fast exact algorithm for L(2,1)-labeling of graphs Fast exact algorithm for L(2,1)-labeling of graphs (en)
skos:notation	RIV/00216208:11320/13:10191010!RIV14-GA0-11320___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GBP202/12/G061)
http://linked.open...iv/cisloPeriodika	September
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Kratochvíl, Jan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	74707
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/13:10191010
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Exponential-time algorithm; 1)-labeling; L(2; Graphs (en)
http://linked.open.../riv/klicoveSlovo	1)-labeling L(2 Exponential-time algorithm Graphs
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[4DE7B66D91D7]
http://linked.open...i/riv/nazevZdroje	Theoretical Computer Science
http://linked.open...in/vavai/riv/obor	IN
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	5 (xsd:int)
http://linked.open...vavai/riv/projekt	Center of excellence - Institute for theoretical computer science (CE-ITI)
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	505
http://linked.open...iv/tvurceVysledku	Kratochvíl, Jan Liedloff, Mathieu Junosza-Szaniawski, Konstanty Rossmanith, Peter Rzazewski, Pawel
http://linked.open...ain/vavai/riv/wos	000325905200006
issn	0304-3975
number of pages	13 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.tcs.2012.06.037
http://localhost/t...ganizacniJednotka	11320

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