The multi-source beachcombers’ problem

Jurek Czyzowicz, Leszek Gąsieniec, Konstantinos Georgiou, Evangelos Kranakis, Fraser MacQuarrie

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

The Beachcombers’ Problem (c.f. [1]) is an optimization problem in which a line segment is to be searched by a set of mobile robots, where each robot has a searching speed si and a walking speed wi, such that si < wi. We explore a natural generalization of the Beachcombers’ Problem, the t-Source Beachcombers’ Problem (t-SBP), where the robots are not constrained to start at a single source: Consider n mobile robots labelled 1, 2,..., n. We choose t sources and we assign each robot to one of them. The problem is to choose the sources and develop mobility schedules (algorithms) for the robots which maximizes the speed of the fleet, or minimize the time that the robots need to collectively search the domain. We propose several algorithms for solving problems of this nature. We prove that 2-SBP is NP-hard even when the robots have identical walking speeds. This contrasts with the case when the robots have identical search speeds, where we give a polynomial time algorithm for t-SBP. We also give a 0.5569-approximation for 2-SBP with arbitrary walking and searching speeds. For t-SBP with arbitrary walking and searching speeds, we give an oblivious randomized algorithm and prove that it provides an expected 1−1/e approximation, asymptotically in t.

Original languageEnglish (US)
Title of host publicationAlgorithms for Sensor Systems - 10th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2014, Revised Selected Papers
EditorsJie Gao, Sándor P. Fekete, Alon Efrat, Yanyong Zhang
PublisherSpringer Verlag
Pages3-21
Number of pages19
ISBN (Electronic)9783662460177
DOIs
StatePublished - Jan 1 2015
Externally publishedYes
Event10th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2014 - Wroclaw, Poland
Duration: Sep 12 2014Sep 12 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8847
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference10th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2014
CountryPoland
CityWroclaw
Period9/12/149/12/14

Keywords

  • Algorithm
  • Approximation
  • Mobile robots
  • Partitioning
  • Randomized
  • Schedule
  • Searching
  • Segment
  • Speed
  • Walking

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Czyzowicz, J., Gąsieniec, L., Georgiou, K., Kranakis, E., & MacQuarrie, F. (2015). The multi-source beachcombers’ problem. In J. Gao, S. P. Fekete, A. Efrat, & Y. Zhang (Eds.), Algorithms for Sensor Systems - 10th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2014, Revised Selected Papers (pp. 3-21). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8847). Springer Verlag. https://doi.org/10.1007/978-3-662-46018-4_1