Information Processing Letters
Discrete Mathematics
Online computation and competitive analysis
Online computation and competitive analysis
Online conflict-free coloring for intervals
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Conflict-Free Coloring of Points and Simple Regions in the Plane
Discrete & Computational Geometry
Conflict-free colorings of shallow discs
Proceedings of the twenty-second annual symposium on Computational geometry
How to play a coloring game against a color-blind adversary
Proceedings of the twenty-second annual symposium on Computational geometry
Conflict-free coloring for intervals: from offline to online
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Conflict-free coloring for rectangle ranges using O(n.382) colors
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Online Conflict-Free Coloring for Intervals
SIAM Journal on Computing
On The Chromatic Number of Geometric Hypergraphs
SIAM Journal on Discrete Mathematics
Conflict-Free colorings of rectangles ranges
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Online conflict-free colorings for hypergraphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Conflict-free colourings of graphs and hypergraphs
Combinatorics, Probability and Computing
Online conflict-free colouring for hypergraphs
Combinatorics, Probability and Computing
Graph unique-maximum and conflict-free colorings
Journal of Discrete Algorithms
Ordered coloring grids and related graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Graph unique-maximum and conflict-free colorings
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Unique-maximum and conflict-free coloring for hypergraphs and tree graphs
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
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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.