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Label-guided graph exploration by a finite automaton

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David PelegAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 4, Issue 4

Article No.: 42, Pages 1 - 18

https://doi.org/10.1145/1383369.1383373

Published: 22 August 2008 Publication History

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Abstract

A finite automaton, simply referred to as a robot, has to explore a graph, that is, visit all the nodes of the graph. The robot has no a priori knowledge of the topology of the graph, nor of its size. It is known that for any k-state robot, there exists a graph of maximum degree 3 that the robot cannot explore. This article considers the effects of allowing the system designer to add short labels to the graph nodes in a preprocessing stage, for helping the exploration by the robot. We describe an exploration algorithm that, given appropriate 2-bit labels (in fact, only 3-valued labels), allows a robot to explore all graphs. Furthermore, we describe a suitable labeling algorithm for generating the required labels in linear time. We also show how to modify our labeling scheme so that a robot can explore all graphs of bounded degree, given appropriate 1-bit labels. In other words, although there is no robot able to explore all graphs of maximum degree 3, there is a robot R, and a way to color in black or white the nodes of any bounded-degree graph G, so that R can explore the colored graph G. Finally, we give impossibility results regarding graph exploration by a robot with no internal memory (i.e., a single-state automaton).

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Label-guided graph exploration by a finite automaton

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 4, Issue 4

August 2008

264 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1383369

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 22 August 2008

Accepted: 01 November 2007

Revised: 01 November 2007

Received: 01 August 2006

Published in TALG Volume 4, Issue 4

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Moses Jr. WRedlich A(2024)Dispersion, Capacitated Nodes, and the Power of a Trusted ShepherdProceedings of the 25th International Conference on Distributed Computing and Networking10.1145/3631461.3632310(400-405)Online publication date: 4-Jan-2024
https://dl.acm.org/doi/10.1145/3631461.3632310
Pattanayak DBhagat SGan Chaudhuri SMolla A(2024)Maximal Independent Set via Mobile AgentsProceedings of the 25th International Conference on Distributed Computing and Networking10.1145/3631461.3631543(74-83)Online publication date: 4-Jan-2024
https://dl.acm.org/doi/10.1145/3631461.3631543
Himani Pandit S(2024)Optimal Dispersion in Triangular Grids: Achieving Efficiency Without Prior KnowledgeDistributed Computing and Intelligent Technology10.1007/978-3-031-81404-4_7(75-91)Online publication date: 31-Dec-2024
https://doi.org/10.1007/978-3-031-81404-4_7
Molla AMondal KMoses W(2023)Fast Deterministic Gathering with Detection on Arbitrary Graphs: The Power of Many Robots2023 IEEE International Parallel and Distributed Processing Symposium (IPDPS)10.1109/IPDPS54959.2023.00015(47-57)Online publication date: May-2023
https://doi.org/10.1109/IPDPS54959.2023.00015
Bu GLotker ZPotop-Butucaru MRabie M(2023)Lower and upper bounds for deterministic convergecast with labeling schemesTheoretical Computer Science10.1016/j.tcs.2023.113775952(113775)Online publication date: Mar-2023
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Das ABose KSau B(2023)Memory optimal dispersion by anonymous mobile robotsDiscrete Applied Mathematics10.1016/j.dam.2023.07.005340:C(171-182)Online publication date: 15-Dec-2023
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Pattanayak DSharma GMandal P(2023)Dispersion of Mobile Robots in Spite of FaultsStabilization, Safety, and Security of Distributed Systems10.1007/978-3-031-44274-2_31(414-429)Online publication date: 30-Sep-2023
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Böckenhauer HFrei FUnger WWehner D(2023)Zero-Memory Graph Exploration with Unknown InportsStructural Information and Communication Complexity10.1007/978-3-031-32733-9_11(246-261)Online publication date: 25-May-2023
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Chand PKumar MMolla ASivasubramaniam S(2023)Fault-Tolerant Dispersion of Mobile RobotsAlgorithms and Discrete Applied Mathematics10.1007/978-3-031-25211-2_3(28-40)Online publication date: 26-Jan-2023
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Kshemkalyani AMolla ASharma G(2022)Dispersion of mobile robots using global communicationJournal of Parallel and Distributed Computing10.1016/j.jpdc.2021.11.007161:C(100-117)Online publication date: 1-Mar-2022
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Graph exploration by a finite automaton