Linear search by a pair of distinct-speed robots

Evangelos Bampas, Jurek Czyzowicz, Leszek Gąsieniec, David Ilcinkas, Ralf Klasing, Tomasz Kociumaka, Dominik Pająk

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

7 Scopus citations

Abstract

Two mobile robots are initially placed at the same point on an infinite line. Each robot may move on the line in either direction not exceeding its maximal speed. The robots need to find a stationary target placed at an unknown location on the line. The search is completed when both robots arrive at the target point. The target is discovered at the moment when either robot arrives at its position. The robot knowing the placement of the target may communicate it to the other robot. We look for the algorithm with the shortest possible search time (i.e. the worst-case time at which both robots meet at the target) measured as a function of the target distance from the origin (i.e. the time required to travel directly from the starting point to the target at unit velocity). We consider two standard models of communication between the robots, namely wireless communication and communication by meeting. In the case of communication by meeting, a robot learns about the target while sharing the same location with the robot possessing this knowledge. We propose here an optimal search strategy for two robots including the respective lower bound argument, for the full spectrum of their maximal speeds. This extends the main result of Chrobak et al. (SOFSEM 2015) referring to the exact complexity of the problem for the case when the speed of the slower robot is at least one third of the faster one. In addition, we consider also the wireless communication model, in which a message sent by one robot is instantly received by the other robot, regardless of their current positions on the line. In this model, we design an optimal strategy whenever the faster robot is at most 6 times faster than the slower one.

Original languageEnglish (US)
Title of host publicationStructural Information and Communication Complexity - 23rd International Colloquium, SIROCCO 2016, Revised Selected Papers
EditorsJukka Suomela
PublisherSpringer Verlag
Pages195-211
Number of pages17
ISBN (Print)9783319483139
DOIs
StatePublished - Jan 1 2016
Event23rd International Colloquium on Structural Information and Communication Complexity, SIROCCO 2016 - Helsinki, Finland
Duration: Jul 19 2016Jul 21 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9988 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd International Colloquium on Structural Information and Communication Complexity, SIROCCO 2016
CountryFinland
CityHelsinki
Period7/19/167/21/16

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Bampas, E., Czyzowicz, J., Gąsieniec, L., Ilcinkas, D., Klasing, R., Kociumaka, T., & Pająk, D. (2016). Linear search by a pair of distinct-speed robots. In J. Suomela (Ed.), Structural Information and Communication Complexity - 23rd International Colloquium, SIROCCO 2016, Revised Selected Papers (pp. 195-211). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9988 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-48314-6_13