2026-07-31T17:39:41Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15783 2024-03-06T10:56:09Z ddc:004 open_access

Near-Optimal Dispersion on Arbitrary Anonymous Graphs Kshemkalyani, Ajay D. Sharma, Gokarna Distributed algorithms Multi-agent systems Mobile robots Local communication Dispersion Exploration Time and memory complexity 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 𝓁) time storing Θ(log(k+Δ)) bits at each robot, where 𝓁 ≤ 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 𝓁) 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ajay D. Kshemkalyani and Gokarna Sharma 2022 Is Part Of LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.OPODIS.2021.8 urn:nbn:de:0030-drops-157837 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.8 eng https://creativecommons.org/licenses/by/4.0/legalcode