### Abstract

The SINR model for the quality of wireless connections has been the subject of extensive recent study. It attempts to predict whether a particular transmitter is heard at a specific location, in a setting consisting of n simultaneous transmitters and background noise. The SINR model gives rise to a natural geometric object, the SINR diagram, which partitions the space into n regions where each of the transmitters can be heard and the remaining space where no transmitter can be heard. Efficient point location in the SINR diagram, i. e., being able to build a data structure that facilitates determining, for a query point, whether any transmitter is heard there, and if so, which one, has been recently investigated in several papers. These planar data structures are constructed in time at least quadratic in n and support logarithmic-time approximate queries. Moreover, the performance of some of the proposed structures depends strongly not only on the number n of transmitters and on the approximation parameter ε, but also on some geometric parameters that cannot be bounded a priori as a function of n or ε. In this paper, we address the question of batched point location queries, i. e., answering many queries simultaneously. Specifically, in one dimension, we can answer n queries exactly in amortized polylogarithmic time per query, while in the plane we can do it approximately. All these results can handle arbitrary power assignments to the transmitters. Moreover, the amortized query time in these results depends only on n and ε. Finally, these results demonstrate the (so far underutilized) power of combining algebraic tools with those of computational geometry and other fields.

Original language | English (US) |
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Title of host publication | Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings |

Publisher | Springer Verlag |

Pages | 65-77 |

Number of pages | 13 |

Volume | 9134 |

ISBN (Print) | 9783662476710 |

DOIs | |

State | Published - 2015 |

Event | 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 - Kyoto, Japan Duration: Jul 6 2015 → Jul 10 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9134 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 |
---|---|

Country | Japan |

City | Kyoto |

Period | 7/6/15 → 7/10/15 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings*(Vol. 9134, pp. 65-77). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9134). Springer Verlag. https://doi.org/10.1007/978-3-662-47672-7_6

**Batched point location in sinr diagrams via algebraic tools.** / Aronov, Boris; Katz, Matthew J.

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

*Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings.*vol. 9134, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9134, Springer Verlag, pp. 65-77, 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015, Kyoto, Japan, 7/6/15. https://doi.org/10.1007/978-3-662-47672-7_6

}

TY - GEN

T1 - Batched point location in sinr diagrams via algebraic tools

AU - Aronov, Boris

AU - Katz, Matthew J.

PY - 2015

Y1 - 2015

N2 - The SINR model for the quality of wireless connections has been the subject of extensive recent study. It attempts to predict whether a particular transmitter is heard at a specific location, in a setting consisting of n simultaneous transmitters and background noise. The SINR model gives rise to a natural geometric object, the SINR diagram, which partitions the space into n regions where each of the transmitters can be heard and the remaining space where no transmitter can be heard. Efficient point location in the SINR diagram, i. e., being able to build a data structure that facilitates determining, for a query point, whether any transmitter is heard there, and if so, which one, has been recently investigated in several papers. These planar data structures are constructed in time at least quadratic in n and support logarithmic-time approximate queries. Moreover, the performance of some of the proposed structures depends strongly not only on the number n of transmitters and on the approximation parameter ε, but also on some geometric parameters that cannot be bounded a priori as a function of n or ε. In this paper, we address the question of batched point location queries, i. e., answering many queries simultaneously. Specifically, in one dimension, we can answer n queries exactly in amortized polylogarithmic time per query, while in the plane we can do it approximately. All these results can handle arbitrary power assignments to the transmitters. Moreover, the amortized query time in these results depends only on n and ε. Finally, these results demonstrate the (so far underutilized) power of combining algebraic tools with those of computational geometry and other fields.

AB - The SINR model for the quality of wireless connections has been the subject of extensive recent study. It attempts to predict whether a particular transmitter is heard at a specific location, in a setting consisting of n simultaneous transmitters and background noise. The SINR model gives rise to a natural geometric object, the SINR diagram, which partitions the space into n regions where each of the transmitters can be heard and the remaining space where no transmitter can be heard. Efficient point location in the SINR diagram, i. e., being able to build a data structure that facilitates determining, for a query point, whether any transmitter is heard there, and if so, which one, has been recently investigated in several papers. These planar data structures are constructed in time at least quadratic in n and support logarithmic-time approximate queries. Moreover, the performance of some of the proposed structures depends strongly not only on the number n of transmitters and on the approximation parameter ε, but also on some geometric parameters that cannot be bounded a priori as a function of n or ε. In this paper, we address the question of batched point location queries, i. e., answering many queries simultaneously. Specifically, in one dimension, we can answer n queries exactly in amortized polylogarithmic time per query, while in the plane we can do it approximately. All these results can handle arbitrary power assignments to the transmitters. Moreover, the amortized query time in these results depends only on n and ε. Finally, these results demonstrate the (so far underutilized) power of combining algebraic tools with those of computational geometry and other fields.

UR - http://www.scopus.com/inward/record.url?scp=84946076419&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84946076419&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-47672-7_6

DO - 10.1007/978-3-662-47672-7_6

M3 - Conference contribution

SN - 9783662476710

VL - 9134

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 65

EP - 77

BT - Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings

PB - Springer Verlag

ER -