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.
@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} }
Feedback for Dagstuhl Publishing