Network exploration by silent and oblivious robots

Jérémie Chalopin*, Paola Flocchini, Bernard Mans, Nicola Santoro

*Corresponding author for this work

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

33 Citations (Scopus)

Abstract

In this paper we investigate the basic problem of Exploration of a graph by a group of identical mobile computational entities, called robots, operating autonomously and asynchronously. In particular we are concerned with what graphs can be explored, and how, if the robots do not remember the past and have no explicit means of communication. This model of robots is used when the spatial universe in which the robots operate is continuous (e.g., a curve, a polygonal region, a plane, etc.). The case when the spatial universe is discrete (i.e., a graph) has been also studied but only for the classes of acyclic graphs and of simple cycles. In this paper we consider networks of arbitrary topology modeled as connected graphs with local orientation (locally distinct edge labels). We concentrate on class Hk of asymmetric configurations with k robots. Our results indicate that the explorability of graphs in this class depends on the number k of robots participating in the exploration. In particular, exploration is impossible for k<3 robots. When there are only k=3 robots, only a subset of H3 can be explored; we provide a complete characterization of the networks that can be explored. When there are k=4 robots, we prove that all networks in H4 can be explored. Finally, we prove that for any odd k>4 all networks in Hk can be explored by presenting a general algorithm. The determination of which networks can be explored when k>4 is even, is still open but can be reduced to the existence of a gathering algorithm for Hk.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science
Subtitle of host publication36th International Workshop, WG 2010, Zarós, Crete, Greece, June 28-30, 2010, Revised Papers
EditorsDimitrios M. Thilikos
Place of PublicationBerlin; Heidelberg
PublisherSpringer, Springer Nature
Pages208-219
Number of pages12
ISBN (Print)3642169252, 9783642169250
DOIs
Publication statusPublished - 2010
Event36th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2010 - Zaros, Crete, Greece
Duration: 28 Jun 201030 Jun 2010

Publication series

NameLecture Notes in Computer Science
Volume6410
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other36th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2010
CountryGreece
CityZaros, Crete
Period28/06/1030/06/10

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  • Cite this

    Chalopin, J., Flocchini, P., Mans, B., & Santoro, N. (2010). Network exploration by silent and oblivious robots. In D. M. Thilikos (Ed.), Graph-Theoretic Concepts in Computer Science: 36th International Workshop, WG 2010, Zarós, Crete, Greece, June 28-30, 2010, Revised Papers (pp. 208-219). (Lecture Notes in Computer Science; Vol. 6410). Berlin; Heidelberg: Springer, Springer Nature. https://doi.org/10.1007/978-3-642-16926-7_20