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A Tight Lower Bound for Semi-Synchronous Collaborative Grid Exploration

Authors Sebastian Brandt, Jara Uitto, Roger Wattenhofer

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Author Details

Sebastian Brandt
  • ETH Zürich, Switzerland
Jara Uitto
  • ETH Zürich, Switzerland
Roger Wattenhofer
  • ETH Zürich, Switzerland

Funding

  • Uitto, Jara: Partially supported by ERC Grant No. 336495 (ACDC).

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Sebastian Brandt, Jara Uitto, and Roger Wattenhofer. A Tight Lower Bound for Semi-Synchronous Collaborative Grid Exploration. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.DISC.2018.13

Abstract

Recently, there has been a growing interest in grid exploration by agents with limited capabilities. We show that the grid cannot be explored by three semi-synchronous finite automata, answering an open question by Emek et al. [TCS'15] in the negative.
In the setting we consider, time is divided into discrete steps, where in each step, an adversarially selected subset of the agents executes one look-compute-move cycle. The agents operate according to a shared finite automaton, where every agent is allowed to have a distinct initial state. The only means of communication is to sense the states of the agents sharing the same grid cell. The agents are equipped with a global compass and whenever an agent moves, the destination cell of the movement is chosen by the agent's automaton from the set of neighboring grid cells. In contrast to the four agent protocol by Emek et al., we show that three agents do not suffice for grid exploration.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Mobile agents
Keywords
  • Finite automata
  • Graph exploration
  • Mobile robots

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