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

Authors:
Ke Chen;Haim Kaplan;Micha Sharir
Affiliations:
University of Illinois at Urbana-Champaign, Urbana, IL;Tel-Aviv University, Tel-Aviv, Israel;Tel-Aviv University, Tel-Aviv, Israel
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2009

Citing 11
Cited 3

Online computation and competitive analysis

Online computation and competitive analysis
Coloring graphs with sparse neighborhoods

Journal of Combinatorial Theory Series B
A unifying look at data structures

Communications of the ACM
Conflict-Free Colorings of Simple Geometric Regions with Applications to Frequency Assignment in Cellular Networks

SIAM Journal on Computing
Conflict-Free Coloring of Points and Simple Regions in the Plane

Discrete & 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
Online conflict-free colorings for hypergraphs

ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming

Dynamic Offline Conflict-Free Coloring for Unit Disks

Approximation and Online Algorithms
Online conflict-free colouring for hypergraphs

Combinatorics, Probability and Computing
The potential to improve the choice: list conflict-free coloring for geometric hypergraphs

Proceedings of the twenty-seventh annual symposium on Computational geometry

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present randomized algorithms for online conflict-free coloring (CF in short) of points in the plane, with respect to halfplanes, congruent disks, and nearly-equal axis-parallel rectangles. In all three cases, the coloring algorithms use O(log n) colors, with high probability. We also present a deterministic algorithm for online CF coloring of points in the plane with respect to nearly-equal axis-parallel rectangles, using O(log3n) colors. This is the first efficient (i.e, using polylog(n) colors) deterministic online CF coloring algorithm for this problem.