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Online Conflict‐Free Coloring for Intervals

2007
*
SIAM journal on computing (Print)
*

be

doi:10.1137/s0097539704446682
fatcat:sthlrzviavcbrccdzhfu7opehq
*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 ...##
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Deterministic conflict-free coloring for intervals

2008
*
ACM Transactions on Algorithms
*

We concentrate on a special case of the problem, called

doi:10.1145/1383369.1383375
fatcat:d4z5mhfzfrh6fgrkmwjmlh35ze
*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. ...##
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Conflict-free coloring for intervals

2006
*
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures - SPAA '06
*

This problem is called

doi:10.1145/1148109.1148133
dblp:conf/spaa/Bar-NoyCS06
fatcat:evuoevrsbvayjj4nqzua3nhfaq
*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. ...##
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Fully-Dynamic and Kinetic Conflict-Free Coloring of Intervals with Respect to Points
[article]

2019
*
arXiv
*
pre-print

We introduce the fully-dynamic

arXiv:1701.03388v2
fatcat:hznnt7vsi5db3cnaysx36koesq
*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*. ...##
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Fully-Dynamic and Kinetic Conflict-Free Coloring of Intervals with Respect to Points

2017
*
International Symposium on Algorithms and Computation
*

Dynamic and kinetic

doi:10.4230/lipics.isaac.2017.26
dblp:conf/isaac/BergL0RRW17
fatcat:n3mmigimlfbf5mo46lgy7bv47q
*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. ...##
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Conflict-free coloring with respect to a subset of intervals
[article]

2012
*
arXiv
*
pre-print

Given a hypergraph H = (V, E), a

arXiv:1204.6422v1
fatcat:lx57sq2lxnfxzcg2z5rbb5gboa
*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. ...##
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Conflict-free coloring with respect to a subset of intervals

2013
*
International Journal of Research Studies in Computing
*

We provide an algorithm

doi:10.5861/ijrsc.2013.547
fatcat:li6fbacwlrfnnenvlqtq4hu2wm
*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*. ...##
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Conflict-Free Coloring of Intersection Graphs
[article]

2017
*
arXiv
*
pre-print

A

arXiv:1709.03876v1
fatcat:ssd4liw3sncb5peerltvokuora
*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. ...##
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How to play a coloring game against a color-blind adversary

2006
*
Proceedings of the twenty-second annual symposium on Computational geometry - SCG '06
*

We study the problem of

doi:10.1145/1137856.1137865
dblp:conf/compgeom/Chen06
fatcat:2shpi6kq45fedbnsz2cm7sejji
*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*. ...##
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An Optimal Algorithm for Conflict-Free Coloring for Tree of Rings
[article]

2012
*
arXiv
*
pre-print

An optimal algorithm is presented about

arXiv:1203.2414v1
fatcat:wsfhx4rcvrhqlhcdt2ogtu7id4
*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] . ...##
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An Optimal Algorithm for Conflict-Free Coloring for Tree of Rings

2012
*
Computer Science & Engineering An International Journal
*

An optimal algorithm is presented about

doi:10.5121/cseij.2012.2101
fatcat:g66n3ftkunfhtfxde5asul5e2u
*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] . ...##
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Conflict-Free Coloring and its Applications
[article]

2012
*
arXiv
*
pre-print

A

arXiv:1005.3616v3
fatcat:mhap6v2hsjcvdh7s424vxgi5jm
*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. ...##
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Online conflict-free coloring for halfplanes, congruent disks, and axis-parallel rectangles

2009
*
ACM Transactions on Algorithms
*

We present randomized algorithms

doi:10.1145/1497290.1497292
fatcat:uadt2gxz2bgnhkhge4ukkeu3q4
*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. ...##
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Conflict-Free Coloring and its Applications
[chapter]

2013
*
Bolyai Society Mathematical Studies
*

A

doi:10.1007/978-3-642-41498-5_12
fatcat:gjf6tvt5yvgn3hlhuc3fcj3rda
*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. ...##
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Online hypergraph coloring with rejection

2015
*
Acta Universitatis Sapientiae: Informatica
*

We consider proper and

doi:10.1515/ausi-2015-0009
fatcat:y5dqfoxo5rapzkw6s5gi32gska
*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. ...
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