### Abstract

Given a set of points P ⊆ ℝ ^{2}, a conflict-free coloring of P w. r. t. rectangle ranges is an assignment of colors to points of P, such that each nonempty axis-parallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T. This notion has been the subject of recent interest and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to base stations (points) such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in ℝ ^{2} can be conflict-free colored with O(n ^{β*+o(1)}) colors in expected polynomial time, where.

Original language | English (US) |
---|---|

Pages (from-to) | 39-52 |

Number of pages | 14 |

Journal | Discrete and Computational Geometry |

Volume | 48 |

Issue number | 1 |

DOIs | |

State | Published - Jul 1 2012 |

### Fingerprint

### Keywords

- Axis-parallel rectangles
- Boundary sets
- Conflict-free coloring
- Frequency assignment in wireless networks
- Monotone sequences

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Cite this

^{.382}) colors.

*Discrete and Computational Geometry*,

*48*(1), 39-52. https://doi.org/10.1007/s00454-012-9425-5

**Conflict-free coloring for rectangle ranges using O(n ^{.382}) colors.** / Ajwani, Deepak; Elbassioni, Khaled; Govindarajan, Sathish; Ray, Saurabh.

Research output: Contribution to journal › Article

^{.382}) colors',

*Discrete and Computational Geometry*, vol. 48, no. 1, pp. 39-52. https://doi.org/10.1007/s00454-012-9425-5

^{.382}) colors. Discrete and Computational Geometry. 2012 Jul 1;48(1):39-52. https://doi.org/10.1007/s00454-012-9425-5

}

TY - JOUR

T1 - Conflict-free coloring for rectangle ranges using O(n .382) colors

AU - Ajwani, Deepak

AU - Elbassioni, Khaled

AU - Govindarajan, Sathish

AU - Ray, Saurabh

PY - 2012/7/1

Y1 - 2012/7/1

N2 - Given a set of points P ⊆ ℝ 2, a conflict-free coloring of P w. r. t. rectangle ranges is an assignment of colors to points of P, such that each nonempty axis-parallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T. This notion has been the subject of recent interest and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to base stations (points) such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in ℝ 2 can be conflict-free colored with O(n β*+o(1)) colors in expected polynomial time, where.

AB - Given a set of points P ⊆ ℝ 2, a conflict-free coloring of P w. r. t. rectangle ranges is an assignment of colors to points of P, such that each nonempty axis-parallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T. This notion has been the subject of recent interest and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to base stations (points) such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in ℝ 2 can be conflict-free colored with O(n β*+o(1)) colors in expected polynomial time, where.

KW - Axis-parallel rectangles

KW - Boundary sets

KW - Conflict-free coloring

KW - Frequency assignment in wireless networks

KW - Monotone sequences

UR - http://www.scopus.com/inward/record.url?scp=84860881461&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860881461&partnerID=8YFLogxK

U2 - 10.1007/s00454-012-9425-5

DO - 10.1007/s00454-012-9425-5

M3 - Article

VL - 48

SP - 39

EP - 52

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 1

ER -