Efficient Dispersion of Mobile Robots on Graphs

TL;DR

This paper introduces three efficient algorithms for dispersing multiple mobile robots on graphs, optimizing for memory and time, applicable to various system models and with real-world relevance.

Contribution

It presents novel algorithms for robot dispersion on graphs that are efficient in memory and time, adaptable to synchronous and asynchronous systems.

Findings

Algorithms run in O(m) steps, with O(k log Δ) bits per robot.

Effective in both synchronous and asynchronous models.

Applicable to real-world scenarios like electric vehicle recharging stations.

Abstract

The dispersion problem on graphs requires $k$ robots placed arbitrarily at the $n$ nodes of an anonymous graph, where $k \leq n$, to coordinate with each other to reach a final configuration in which each robot is at a distinct node of the graph. The dispersion problem is important due to its relationship to graph exploration by mobile robots, scattering on a graph, and load balancing on a graph. In addition, an intrinsic application of dispersion has been shown to be the relocation of self-driven electric cars (robots) to recharge stations (nodes). We propose three efficient algorithms to solve dispersion on graphs. Our algorithms require $O(k \log \Delta)$ bits at each robot, and $O(m)$ steps running time, where $m$ is the number of edges and $\Delta$ is the degree of the graph. The algorithms differ in whether they address the synchronous or the asynchronous system model, and in what, where, and how data structures are maintained.