License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.OPODIS.2021.8
URN: urn:nbn:de:0030-drops-157837
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15783/
Kshemkalyani, Ajay D. ;
Sharma, Gokarna
Near-Optimal Dispersion on Arbitrary Anonymous Graphs
Abstract
Given an undirected, anonymous, port-labeled graph of n memory-less nodes, m edges, and degree Δ, we consider the problem of dispersing k ≤ n robots (or tokens) positioned initially arbitrarily on one or more nodes of the graph to exactly k different nodes of the graph, one on each node. The objective is to simultaneously minimize time to achieve dispersion and memory requirement at each robot. If all k robots are positioned initially on a single node, depth first search (DFS) traversal solves this problem in O(min{m,kΔ}) time with Θ(log(k+Δ)) bits at each robot. However, if robots are positioned initially on multiple nodes, the best previously known algorithm solves this problem in O(min{m,kΔ}⋅ log ?) time storing Θ(log(k+Δ)) bits at each robot, where ? ≤ k/2 is the number of multiplicity nodes in the initial configuration. In this paper, we present a novel multi-source DFS traversal algorithm solving this problem in O(min{m,kΔ}) time with Θ(log(k+Δ)) bits at each robot, improving the time bound of the best previously known algorithm by O(log ?) and matching asymptotically the single-source DFS traversal bounds. This is the first algorithm for dispersion that is optimal in both time and memory in arbitrary anonymous graphs of constant degree, Δ = O(1). Furthermore, the result holds in both synchronous and asynchronous settings.
BibTeX - Entry
@InProceedings{kshemkalyani_et_al:LIPIcs.OPODIS.2021.8,
author = {Kshemkalyani, Ajay D. and Sharma, Gokarna},
title = {{Near-Optimal Dispersion on Arbitrary Anonymous Graphs}},
booktitle = {25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
pages = {8:1--8:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-219-8},
ISSN = {1868-8969},
year = {2022},
volume = {217},
editor = {Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/15783},
URN = {urn:nbn:de:0030-drops-157837},
doi = {10.4230/LIPIcs.OPODIS.2021.8},
annote = {Keywords: Distributed algorithms, Multi-agent systems, Mobile robots, Local communication, Dispersion, Exploration, Time and memory complexity}
}
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Keywords: |
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Distributed algorithms, Multi-agent systems, Mobile robots, Local communication, Dispersion, Exploration, Time and memory complexity |
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Collection: |
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25th International Conference on Principles of Distributed Systems (OPODIS 2021) |
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Issue Date: |
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2022 |
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Date of publication: |
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28.02.2022 |
