Fault-tolerant dispersion of mobile robots

Article Type

Research Article

Publication Title

Discrete Applied Mathematics

Abstract

The dispersion problem, where mobile robots spread evenly across a graph, has recently gained attention for its potential to solve a variety of problems in distributed robotics such as relocating autonomous vehicles to garages or charging stations, covering a region, guarding, load balancing, etc. Dispersion has also been recognized as a foundational primitive for solving a variety of distributed graph problems. Recent studies demonstrate its utility in facilitating computations such as dominating set construction [8], maximal independent set (MIS) formation [29], leader election & computing a minimum spanning tree (MST) [16], triangle counting [6], etc. These works assume a robust system in which all robots are fault-free. However, in real-world systems, faults are inevitable, and it is essential to design mechanisms that ensure unexpected crashes do not obstruct the dispersion process, which forms a critical foundation for addressing these problems. In this paper, we consider the mobile robot dispersion problem in the presence of crash faults. Mobile robot dispersion consists of k≤n robots operating in an n-node anonymous graph. The goal is to ensure that, regardless of the initial placement of the robots across the nodes, the final configuration places at most one robot per node. In a crash-fault setting, up to f≤k robots may fail arbitrarily by crashing, thereby losing all stored information and becoming incapable of communication. In this paper, we solve the dispersion problem under crash-fault conditions by analysing two different initial configurations: (i) the rooted configuration, and (ii) the arbitrary configuration. In the rooted case, all robots start at a single node. In contrast, the arbitrary configuration allows the robots to be initially distributed across the graph in l2) rounds, improving upon the prior results by [30,31]. For the arbitrary configuration, we present an algorithm that solves dispersion in O((f+l)⋅min(m,kΔ,k2)) rounds, assuming the number of edges m and the maximum degree Δ of the graph are known to the robots. Both our algorithms uses O(log(k+Δ)) bits of memory per robot.

First Page

299

Last Page

313

DOI

10.1016/j.dam.2025.06.068

Publication Date

12-31-2025

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