### 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 non-empty 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 bases 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 (n^{Β+}) colors in expected polynomial time, for any arbitrarily small > 0 and Β = 3?5<over>2 < 0.382. This improves upon the previously known bound of O(nlog log n/ log n).

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

Title of host publication | SPAA'07 |

Subtitle of host publication | Proceedings of the Nineteenth Annual Symposium on Parallelism in Algorithms and Architectures |

Pages | 181-187 |

Number of pages | 7 |

DOIs | |

State | Published - Oct 18 2007 |

Event | SPAA'07: 19th Annual Symposium on Parallelism in Algorithms and Architectures - San Diego, CA, United States Duration: Jun 9 2007 → Jun 11 2007 |

### Other

Other | SPAA'07: 19th Annual Symposium on Parallelism in Algorithms and Architectures |
---|---|

Country | United States |

City | San Diego, CA |

Period | 6/9/07 → 6/11/07 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

^{.382}) colors. In

*SPAA'07: Proceedings of the Nineteenth Annual Symposium on Parallelism in Algorithms and Architectures*(pp. 181-187) https://doi.org/10.1145/1248377.1248406

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

^{.382}) colors. in

*SPAA'07: Proceedings of the Nineteenth Annual Symposium on Parallelism in Algorithms and Architectures.*pp. 181-187, SPAA'07: 19th Annual Symposium on Parallelism in Algorithms and Architectures, San Diego, CA, United States, 6/9/07. https://doi.org/10.1145/1248377.1248406

^{.382}) colors. In SPAA'07: Proceedings of the Nineteenth Annual Symposium on Parallelism in Algorithms and Architectures. 2007. p. 181-187 https://doi.org/10.1145/1248377.1248406

}

TY - GEN

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 - 2007/10/18

Y1 - 2007/10/18

N2 - Given a set of points P R2, a conflict-free coloring of P w.r.t. rectangle ranges is an assignment of colors to points of P, such that each non-empty 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 bases stations (points), such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in R2 can be conflict-free colored with (nΒ+) colors in expected polynomial time, for any arbitrarily small > 0 and Β = 3?52 < 0.382. This improves upon the previously known bound of O(nlog log n/ log n).

AB - Given a set of points P R2, a conflict-free coloring of P w.r.t. rectangle ranges is an assignment of colors to points of P, such that each non-empty 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 bases stations (points), such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in R2 can be conflict-free colored with (nΒ+) colors in expected polynomial time, for any arbitrarily small > 0 and Β = 3?52 < 0.382. This improves upon the previously known bound of O(nlog log n/ log n).

KW - Axis-parallel rectangles

KW - Conflict-free coloring

KW - Dominating sets

KW - Frequency assignment in wireless networks

KW - Monotone sequences

UR - http://www.scopus.com/inward/record.url?scp=35248897157&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35248897157&partnerID=8YFLogxK

U2 - 10.1145/1248377.1248406

DO - 10.1145/1248377.1248406

M3 - Conference contribution

SN - 159593667X

SN - 9781595936677

SP - 181

EP - 187

BT - SPAA'07

ER -