Online Range Assignment Problems

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Abstract

We study two online range assignment problems. In the first problem, introduced by de Berg et al. [4], P is a growing set of transceivers, initially consisting of a single transceiver p1. Upon the arrival of a new transceiver pi, one needs to (re)assign a range to at most one of the ‘previous’ transceivers, so that pi is covered by at least one of them. We adopt the common rule that a transceiver’s range (which is initially 0) can never decrease over time. The cost of such an online range assignment is ∑i=1nρ(pi), where ρ(pi) is the final range assigned to pi, and we wish to compare it with the cost of an optimal offline assignment which satisfies the intermediate coverage requirements. We present several results for this problem, which improve some of the previous results of de Berg et al. [4]. We also introduce a new problem, in which we have a set T of stationary transmitters and an initially-empty set S of mobile receivers. Upon the arrival of a new receiver s, it must first specify its intended route, after which one needs to (re)assign a range to at most one of the transmitters in T, so that s’s route is fully covered by at least one of them. We consider the case where the routes of the receivers are unit line segments and prove a constant factor upper bound on the competitive ratio of our range assignment algorithm.

Original languageAmerican English
Title of host publicationAlgorithms and Complexity - 14th International Conference, CIAC 2025, Proceedings
EditorsIrene Finocchi, Loukas Georgiadis
PublisherSpringer Science and Business Media Deutschland GmbH
Pages68-82
Number of pages15
ISBN (Print)9783031929311
DOIs
StatePublished - 1 Jan 2025
Event14th International Conference on Algorithms and Complexity, CIAC 2025 - Rome, Italy
Duration: 10 Jun 202512 Jun 2025

Publication series

NameLecture Notes in Computer Science
Volume15679 LNCS

Conference

Conference14th International Conference on Algorithms and Complexity, CIAC 2025
Country/TerritoryItaly
CityRome
Period10/06/2512/06/25

Keywords

  • broadcast
  • competitive analysis
  • online algorithms
  • range assignment

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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