Collaborative Dispersion by Silent Robots

Barun Gorain, Partha Sarathi Mandal, Kaushik Mondal, Supantha Pandit

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


In the dispersion problem, a set of k co-located mobile robots must relocate themselves in distinct nodes of an unknown network. The network is modeled as an anonymous graph G= (V, E), where the graph’s nodes are not labeled. The edges incident to a node v with degree d are labeled with port numbers in the range { 0, 1, …, d- 1 } at v. The robots have unique IDs in the range [0, L], where L≥ k, and are initially placed at a source node s. Each robot knows only its ID, however, it does not know the IDs of the other robots or the values of L or k. The task of the dispersion was traditionally achieved based on the assumption of two types of communication abilities: (a) when some robots are at the same node, they can communicate by exchanging messages between them, and (b) any two robots in the network can exchange messages between them. This paper investigates whether this communication ability among co-located robots is absolutely necessary to achieve the dispersion. We established that even in the absence of the ability of communication, the task of the dispersion by a set of mobile robots can be achieved in a much weaker model, where a robot at a node v has the access of following very restricted information at the beginning of any round: (1) am I alone at v? (2) did the number of robots at v increase or decrease compared to the previous round? We propose a deterministic distributed algorithm that achieves the dispersion on any given graph G= (V, E) in time O(klog L+ k2log Δ), where Δ is the maximum degree of a node in G. Further, each robot uses O(log L+ log Δ) additional memory. We also prove that the task of the dispersion cannot be achieved by a set of mobile robots with o(log L+ log Δ) additional memory.

Original languageEnglish
Title of host publicationStabilization, Safety, and Security of Distributed Systems - 24th International Symposium, SSS 2022, Proceedings
EditorsStéphane Devismes, Franck Petit, Karine Altisen, Giuseppe Antonio Di Luna, Antonio Fernandez Anta
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages16
ISBN (Print)9783031210167
StatePublished - 1 Jan 2022
Externally publishedYes
Event24th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2022 - Clermont-Ferrand, France
Duration: 15 Nov 202217 Nov 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13751 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference24th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2022


  • Anonymous graphs
  • Autonomous mobile robots
  • Deterministic algorithm
  • Dispersion
  • Time and memory complexity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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