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Online Conflict‐Free Coloring for Intervals

Ke Chen, Amos Fiat, Haim Kaplan, Meital Levy, Jiří Matoušek, Elchanan Mossel, János Pach, Micha Sharir, Shakhar Smorodinsky, Uli Wagner, Emo Welzl
2007 SIAM journal on computing (Print)  
be conflict-free, in the sense that in every interval I there is a color that appears exactly once in I.  ...  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  ...  The solution of this recurrence is Z k = 1 Lower Bound for Online CF-Coloring in the Plane We finally show that online conflict-free coloring of points in the plane, with respect to disks (of arbitrary  ... 
doi:10.1137/s0097539704446682 fatcat:sthlrzviavcbrccdzhfu7opehq

Deterministic conflict-free coloring for intervals

Amotz Bar-Noy, Panagiotis Cheilaris, Shakhar Smorodinsky
2008 ACM Transactions on Algorithms  
We concentrate on a special case of the problem, called conflict-free coloring for intervals.  ...  We also consider conflict-free coloring only with respect to intervals that contain at least one of the two extreme points.  ...  ACKNOWLEDGMENTS We would like to thank János Pach and David Peleg for helpful discussions concerning the problems studied in this paper.  ... 
doi:10.1145/1383369.1383375 fatcat:d4z5mhfzfrh6fgrkmwjmlh35ze

Conflict-free coloring for intervals

Amotz Bar-Noy, Panagiotis Cheilaris, Shakhar Smorodinsky
2006 Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures - SPAA '06  
This problem is called conflict-free coloring for intervals.  ...  where the vertices appear in some order and the conflict-free prop- *  ...  Acknowledgements We would like to thank János Pach and David Peleg for helpful discussions concerning the problems studied in this paper. We would also like to thank the reviewers for their comments.  ... 
doi:10.1145/1148109.1148133 dblp:conf/spaa/Bar-NoyCS06 fatcat:evuoevrsbvayjj4nqzua3nhfaq

Fully-Dynamic and Kinetic Conflict-Free Coloring of Intervals with Respect to Points [article]

Mark de Berg, Tim Leijsen, André van Renssen, Marcel Roeloffzen, Aleksandar Markovic, Gerhard Woeginger
2019 arXiv   pre-print
We introduce the fully-dynamic conflict-free coloring problem for a set S of intervals in R^1 with respect to points, where the goal is to maintain a conflict-free coloring forS under insertions and deletions  ...  A coloring is conflict-free if for each point p contained in some interval, p is contained in an interval whose color is not shared with any other interval containing p.  ...  For each n > 0, there is a sequence of n intervals for which any online conflict-free coloring requires at least log 2 n + 1 colors.  ... 
arXiv:1701.03388v2 fatcat:hznnt7vsi5db3cnaysx36koesq

Fully-Dynamic and Kinetic Conflict-Free Coloring of Intervals with Respect to Points

Mark De Berg, Tim Leijsen, Aleksandar Markovic, André Van Renssen, Marcel Roeloffzen, Gerhard Woeginger, Marc Herbstritt
2017 International Symposium on Algorithms and Computation  
Dynamic and kinetic conflict-free coloring of intervals with respect to points. arXiv, (1701.03388), [1701.03388].  ...  For each n > 0, there is a sequence of n intervals for which any online conflict-free coloring requires at least log 2 n + 1 colors. Proof.  ...  We reduce the static conflict-free coloring problem for n points with respect to intervals in R 1 to the online problem for coloring intervals with respect to points.  ... 
doi:10.4230/lipics.isaac.2017.26 dblp:conf/isaac/BergL0RRW17 fatcat:n3mmigimlfbf5mo46lgy7bv47q

Conflict-free coloring with respect to a subset of intervals [article]

Panagiotis Cheilaris, Shakhar Smorodinsky
2012 arXiv   pre-print
Given a hypergraph H = (V, E), a coloring of its vertices is said to be conflict-free if for every hyperedge S ∈ E there is at least one vertex in S whose color is distinct from the colors of all other  ...  We provide a polynomial time algorithm for conflict-free coloring any subhypergraph of Hn, we show that the algorithm has approximation ratio 2, and we prove that our analysis is tight, i.e., there is  ...  We wish to thank Matya Katz and Asaf Levin for helpful discussions concerning the problems studied in this paper.  ... 
arXiv:1204.6422v1 fatcat:lx57sq2lxnfxzcg2z5rbb5gboa

Conflict-free coloring with respect to a subset of intervals

Vinay Kumar Singhal, Akanksha Gupta
2013 International Journal of Research Studies in Computing  
We provide an algorithm for conflict-free coloring any subhypergraph of H n . i.e. any subset of possible intervals.  ...  Given a hypergraph H = (V, E), a coloring of its vertices is said to be conflict-free if for every hyperedge S ∈ E there is at least one vertex in S whose color is distinct from the colors of all other  ...  Conflict-free coloring for subset of intervals: In this section, we present an algorithm for conflict-free coloring for subset of intervals.  ... 
doi:10.5861/ijrsc.2013.547 fatcat:li6fbacwlrfnnenvlqtq4hu2wm

Conflict-Free Coloring of Intersection Graphs [article]

Sándor P. Fekete, Phillip Keldenich
2017 arXiv   pre-print
A conflict-free k-coloring of a graph G=(V,E) assigns one of k different colors to some of the vertices such that, for every vertex v, there is a color that is assigned to exactly one vertex among v and  ...  For unit-disk intersection graphs, we prove that it is NP-complete to decide the existence of a conflict-free coloring with one color; we also show that six colors always suffice, using an algorithm that  ...  [12] that presents, among other results, a randomized online algorithm using O(log n) colors to maintain a conflict-free coloring of a set of intervals, or the work of Bar-Nov et al.  ... 
arXiv:1709.03876v1 fatcat:ssd4liw3sncb5peerltvokuora

How to play a coloring game against a color-blind adversary

Ke Chen
2006 Proceedings of the twenty-second annual symposium on Computational geometry - SCG '06  
We study the problem of conflict-free (CF) coloring of a set of points in the plane, in an online fashion, with respect to halfplanes, nearly-equal axis-parallel rectangles, and congruent disks.  ...  As a warm-up exercise, the online CF coloring of points on the line with respect to intervals is also considered.  ...  Theorem 3.3 One can online CF color a sequence of n points on the line, against an oblivious adversary, such that the coloring is conflict-free with respect to intervals.  ... 
doi:10.1145/1137856.1137865 dblp:conf/compgeom/Chen06 fatcat:2shpi6kq45fedbnsz2cm7sejji

An Optimal Algorithm for Conflict-Free Coloring for Tree of Rings [article]

Einollah Pira
2012 arXiv   pre-print
An optimal algorithm is presented about Conflict-Free Coloring for connected subgraphs of tree of rings. Suppose the number of the rings in the tree is |T| and the maximum length of rings is |R|.  ...  A presented algorithm in [1] for a Tree of rings used O(log|T|.log|R|) colors but this algorithm uses O(log|T|+log|R|) colors.  ...  In [5] there is the online version of conflict-free coloring of a hypergraph. The online version of Connected Subgraphs Conflict-Free Coloring in chains was presented in [8] .  ... 
arXiv:1203.2414v1 fatcat:wsfhx4rcvrhqlhcdt2ogtu7id4

An Optimal Algorithm for Conflict-Free Coloring for Tree of Rings

Einollah Pira
2012 Computer Science & Engineering An International Journal  
An optimal algorithm is presented about Conflict-Free Coloring for connected subgraphs of tree of rings. Suppose the number of the rings in the tree is |T| and the maximum length of rings is |R|.  ...  A presented algorithm in [1] for a Tree of rings used O(log|T|.log|R|) colors but this algorithm uses O(log|T|+log|R|) colors.  ...  In [5] there is the online version of conflict-free coloring of a hypergraph. The online version of Connected Subgraphs Conflict-Free Coloring in chains was presented in [8] .  ... 
doi:10.5121/cseij.2012.2101 fatcat:g66n3ftkunfhtfxde5asul5e2u

Conflict-Free Coloring and its Applications [article]

Shakhar Smorodinsky
2012 arXiv   pre-print
A conflict-free coloring of H is an assignment of colors to V such that in each hyperedge e ∈ E there is at least one uniquely-colored vertex.  ...  This notion is an extension of the classical graph coloring.  ...  I would like to thank the two anonymous referees for providing very valuable comments and suggestions.  ... 
arXiv:1005.3616v3 fatcat:mhap6v2hsjcvdh7s424vxgi5jm

Online conflict-free coloring for halfplanes, congruent disks, and axis-parallel rectangles

Ke Chen, Haim Kaplan, Micha Sharir
2009 ACM Transactions on Algorithms  
We present randomized algorithms for online conflict-free coloring of points in the plane, with respect to halfplanes, congruent disks, and nearly-equal axis-parallel rectangles.  ...  This is the first efficient (that is, using polylog(n) colors) deterministic online CF coloring algorithm for this problem.  ...  Acknowledgments The authors thank Sariel Har-Peled for helpful discussions on the problems studied in the paper and useful comments on the manuscript.  ... 
doi:10.1145/1497290.1497292 fatcat:uadt2gxz2bgnhkhge4ukkeu3q4

Conflict-Free Coloring and its Applications [chapter]

Shakhar Smorodinsky
2013 Bolyai Society Mathematical Studies  
A conflict-free coloring of H is an assignment of colors to V such that, in each hyperedge e ∈ E, there is at least one uniquely-colored vertex.  ...  Conflict-free coloring has been the focus of many recent research papers. In this paper, we survey this notion and its combinatorial and algorithmic aspects. large gap between χ cf (H) and χ um (H).  ...  I would like to thank the two anonymous referees for providing very valuable comments and suggestions.  ... 
doi:10.1007/978-3-642-41498-5_12 fatcat:gjf6tvt5yvgn3hlhuc3fcj3rda

Online hypergraph coloring with rejection

Csanád Imreh, Judit Nagy-György
2015 Acta Universitatis Sapientiae: Informatica  
We consider proper and conflict free colorings. We present in each cases optimal online algorithms in the sense that they achieve asymptotically the smallest possible competitive ratio.  ...  The goal is to minimize the sum of the number of the used colors for the accepted vertices and the total penalty paid for the rejected ones.  ...  We can define the problem for both the proper and the conflict free coloring. We consider the online problem.  ... 
doi:10.1515/ausi-2015-0009 fatcat:y5dqfoxo5rapzkw6s5gi32gska
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