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Document
DOI: 10.4230/LIPIcs.ISAAC.2025.35
Anonymous Self-Stabilising Localisation via Spatial Population Protocols

Authors: Leszek Gąsieniec, Łukasz Kuszner, Ehsan Latif, Ramviyas Parasuraman, Paul Spirakis, and Grzegorz Stachowiak

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
In the distributed localisation problem (DLP), n anonymous robots (agents) A_0, ..., A_{n-1} are located at arbitrary points p_0, ..., p_{n-1} ∈ S, where S is a Euclidean space. Initially, each agent A_i operates within its own coordinate system in S, which may be inconsistent with those of other agents. The primary goal in DLP is for agents to reach a consensus on a unified (jointly agreed) coordinate system, in which all agents receive unique labels (coordinates) that accurately reflect the relative distances between all points p_0, ..., p_{n-1} in S. Extensive research on DLP has primarily focus on the feasibility and complexity of achieving consensus when agents have limited access to inter-agent distances, often due to missing or imprecise data. In contrast, this paper proposes a minimalist, computationally efficient distributed computing model where agents can query any pairwise relative positions, if needed. Specifically, we introduce a novel variant of population protocols, referred to as the spatial population protocols model. In this variant each agent can memorise one or a fixed number of coordinates, and when agents A_i and A_j interact, they can not only exchange their current knowledge but also either determine the distance d_{ij} between them in S (distance query model) or obtain the vector v_{ij} spanning points p_i and p_j (vector query model). We propose and analyse several distributed localisation protocols, including: 1) Leader-based localisation protocol with distance queries We propose and analyse two leader-based localisation protocols that stabilise silently in o(n) time. These protocols leverage an efficient solution to the novel concept of multi-contact epidemic, a natural generalisation of the core communication tool in population protocols, known as the one-way epidemic. 2) Self-stabilising leader localisation protocol with distance queries We show how to effectively utilise a leader election mechanism within the leader-based localisation protocol to get a DLP protocol that self-stabilises silently in time O(n(log n/n)^{1/(k+1)}log n) in k-dimensions. 3) Self-stabilising localisation protocol with vector queries We propose and analyse an optimally fast DLP protocol which self-stabilises silently in O(log n) time.
Cite as

Leszek Gąsieniec, Łukasz Kuszner, Ehsan Latif, Ramviyas Parasuraman, Paul Spirakis, and Grzegorz Stachowiak. Anonymous Self-Stabilising Localisation via Spatial Population Protocols. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gasieniec_et_al:LIPIcs.ISAAC.2025.35,
  author =	{G\k{a}sieniec, Leszek and Kuszner, {\L}ukasz and Latif, Ehsan and Parasuraman, Ramviyas and Spirakis, Paul and Stachowiak, Grzegorz},
  title =	{{Anonymous Self-Stabilising Localisation via Spatial Population Protocols}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{35:1--35:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.35},
  URN =		{urn:nbn:de:0030-drops-249433},
  doi =		{10.4230/LIPIcs.ISAAC.2025.35},
  annote =	{Keywords: Population Protocols, Distributed Localisation, Spacial Queries, Self-Stabilisation}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.SAND.2025.19
Brief Announcement: Anonymous Distributed Localisation via Spatial Population Protocols

Authors: Leszek Gąsieniec, Łukasz Kuszner, Ehsan Latif, Ramviyas Parasuraman, Paul Spirakis, and Grzegorz Stachowiak

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
In the distributed localization problem (DLP), n anonymous robots (agents) A₀, …, A_{n-1} begin at arbitrary positions p₀, …, p_{n-1} ∈ S, where S is a Euclidean space. Initially, each agent A_i operates within its own coordinate system in S, which may be inconsistent with those of other agents. The primary goal in DLP is for agents to reach a consensus on a unified coordinate system that accurately reflects the relative positions of all points, p₀, …, p_{n-1}, in S. Extensive research on DLP has primarily focused on the feasibility and complexity of achieving consensus when agents have limited access to inter-agent distances, often due to missing or imprecise data. In this paper, however, we examine a minimalist, computationally efficient model of distributed computing in which agents have access to all pairwise distances, if needed. Specifically, we introduce a novel variant of population protocols, referred to as the spatial population protocols model. In this variant each agent can memorise one or a fixed number of coordinates, and when agents A_i and A_j interact, they can not only exchange their current knowledge but also either determine the distance d_{ij} between them in S (distance query model) or obtain the vector v→_{ij} spanning points p_i and p_j (vector query model). We present here a leader-based localisation protocol with distance queries.
Cite as

Leszek Gąsieniec, Łukasz Kuszner, Ehsan Latif, Ramviyas Parasuraman, Paul Spirakis, and Grzegorz Stachowiak. Brief Announcement: Anonymous Distributed Localisation via Spatial Population Protocols. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 19:1-19:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gasieniec_et_al:LIPIcs.SAND.2025.19,
  author =	{G\k{a}sieniec, Leszek and Kuszner, {\L}ukasz and Latif, Ehsan and Parasuraman, Ramviyas and Spirakis, Paul and Stachowiak, Grzegorz},
  title =	{{Brief Announcement: Anonymous Distributed Localisation via Spatial Population Protocols}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{19:1--19:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.19},
  URN =		{urn:nbn:de:0030-drops-230726},
  doi =		{10.4230/LIPIcs.SAND.2025.19},
  annote =	{Keywords: Population Protocols, Distributed Localisation}
}
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