On the minimum cost range assignment problem

Paz Carmi, Lilach Chaitman-Yerushalmi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

We study the problem of assigning transmission ranges to radio stations placed in a d-dimensional (d-D) Euclidean space in order to achieve a strongly connected communication network with minimum total cost, where the cost of transmitting in range r is proportional to rα. While this problem can be solved optimally in 1D, in higher dimensions it is known to be NP-hard for any α ≥ 1. For the 1D version of the problem and α ≥ 1, we propose a new approach that achieves an exact O(n2)-time algorithm. This improves the running time of the best known algorithm by a factor of n. Moreover, we show that this new technique can be utilized for achieving a polynomialtime algorithm for finding the minimum cost range assignment in 1D whose induced communication graph is a t-spanner, for any t ≥ 1. In higher dimensions, finding the optimal range assignment is NPhard; however, it can be approximated within a constant factor. The best known approximation ratio is for the case α = 1, where the approximation ratio is 1.5. We show a new approximation algorithm that breaks the 1.5 ratio.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 26th International Symposium, ISAAC 2015, Proceedings
EditorsKhaled Elbassioni, Kazuhisa Makino
PublisherSpringer Verlag
Pages95-105
Number of pages11
ISBN (Print)9783662489703
DOIs
StatePublished - 1 Jan 2015
Event26th International Symposium on Algorithms and Computation, ISAAC 2015 - Nagoya, Japan
Duration: 9 Dec 201511 Dec 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9472
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference26th International Symposium on Algorithms and Computation, ISAAC 2015
Country/TerritoryJapan
CityNagoya
Period9/12/1511/12/15

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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