2007
DOI: 10.1137/s0097539704446682
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Online Conflict‐Free Coloring for Intervals

Abstract: We consider an online version of the conflict-free coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be conflict-free, in the sense that in every interval I there is a color that appears exactly once in I. We present several deterministic and randomized algorithms for achieving this goal, and analyze their performance, that is, the maximum number of colors that they need to use, as a function of the number n of… Show more

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Cited by 53 publications
(74 citation statements)
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“…Hoffman et al [20] give tight bounds for the conflict-free chromatic art gallery problem under rectangular visibility in orthogonal polygons: Θ(log log n) are sometimes necessary and always sufficient. Chen et al [13] consider the online version of the conflict-free coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be conflict-free. Also in the online scenario, Bar-Nov et al [9] consider a certain class of k-degenerate hypergraphs which sometimes arise as intersection graphs of geometric objects, presenting an online algorithm using O(k log n) colors.…”
Section: Related Workmentioning
confidence: 99%
“…Hoffman et al [20] give tight bounds for the conflict-free chromatic art gallery problem under rectangular visibility in orthogonal polygons: Θ(log log n) are sometimes necessary and always sufficient. Chen et al [13] consider the online version of the conflict-free coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be conflict-free. Also in the online scenario, Bar-Nov et al [9] consider a certain class of k-degenerate hypergraphs which sometimes arise as intersection graphs of geometric objects, presenting an online algorithm using O(k log n) colors.…”
Section: Related Workmentioning
confidence: 99%
“…It was shown in [9] that the static version of this problem can be solved using 1 + log 2 n colors and this is also the best that we can do. For the online case, Chen et al [6] gave an algorithm that uses O(log 2 n) colors. In between the static and the online models, Bar-Noy et al [4] studied two semionline models, namely the dynamic offline model where the entire sequence of the vertices is given but the vertices have to be colored one-by-one according to the order of the sequence and the colors cannot be changed later, and the online absolute position model where the vertices are presented in the online fashion but the positions of all vertices on the line are known, i.e, for every vertex we know how many other vertices are on the left and right of this vertex.…”
Section: Definition 3 (Dual Cf-coloring) Let (X R) Be a Range Spacementioning
confidence: 99%
“…Randomized algorithms have been proposed for the online dual CF-coloring for intervals [6], unit disks [5,7], and hypergraphs (i.e., general range space) [3].…”
Section: Definition 3 (Dual Cf-coloring) Let (X R) Be a Range Spacementioning
confidence: 99%
“…In addition to this practical motivation, this new coloring model has drawn much attention of researchers through its own theoretical interest and such colorings have been the focus of several recent papers [1,4,6,8,9,10,13].…”
Section: Theorem 14 Let R Be a Family Of N Axis-parallel Rectanglesmentioning
confidence: 99%