Deterministic conflict-free coloring for intervals: From offline to online

Bar-Noy, A; Cheilaris, P; Smorodinsky, S

dc.contributor.author	Bar-Noy, A	en
dc.contributor.author	Cheilaris, P	en
dc.contributor.author	Smorodinsky, S	en
dc.date.accessioned	2014-03-01T01:57:06Z
dc.date.available	2014-03-01T01:57:06Z
dc.date.issued	2008	en
dc.identifier.issn	15496325	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/28349
dc.subject	Cellular networks	en
dc.subject	Coloring	en
dc.subject	Conflict free	en
dc.subject	Frequency assignment	en
dc.subject	Online algorithms	en
dc.subject.other	Cellular networks	en
dc.subject.other	Conflict free	en
dc.subject.other	Frequency assignment	en
dc.subject.other	Online algorithms	en
dc.subject.other	Cellular neural networks	en
dc.subject.other	Computer networks	en
dc.subject.other	Graph theory	en
dc.subject.other	Coloring	en
dc.title	Deterministic conflict-free coloring for intervals: From offline to online	en
heal.type	journalArticle	en
heal.identifier.primary	10.1145/1383369.1383375	en
heal.identifier.secondary	http://dx.doi.org/10.1145/1383369.1383375	en
heal.identifier.secondary	44	en
heal.publicationDate	2008	en
heal.abstract	We investigate deterministic algorithms for a frequency assignment problem in cellular networks. The problem can be modeled as a special vertex coloring problem for hypergraphs: In every hyperedge there must exist a vertex with a color that occurs exactly once in the hyperedge (the conflict-free property). We concentrate on a special case of the problem, called conflict-free coloring for intervals. We introduce a hierarchy of four models for the aforesaid problem: (i) static, (ii) dynamic offline, (iii) dynamic online with absolute positions, and (iv) dynamic online with relative positions. In the dynamic offline model, we give a deterministic algorithm that uses at most log3/2 n + 1 &approx; 1.71 log2 n colors and show inputs that force any algorithm to use at least 3 log5 n + 1 1.29 log2 n colors. For the online absolute-positions model, we give a deterministic algorithm that uses at most 3⌈log3 n⌉ 1.89 log2 n colors. To the best of our knowledge, this is the first deterministic online algorithm using O(log n) colors in a nontrivial online model. In the online relative-positions model, we resolve an open problem by showing a tight analysis on the number of colors used by the first-fit greedy online algorithm. We also consider conflict-free coloring only with respect to intervals that contain at least one of the two extreme points. © 2008 ACM.	en
heal.journalName	ACM Transactions on Algorithms	en
dc.identifier.doi	10.1145/1383369.1383375	en
dc.identifier.volume	4	en
dc.identifier.issue	4	en