Connectivity-Preserving Scattering of Mobile Robots with Limited Visibility

The

scattering

problem is a fundamental task for mobile robots, which requires that no two robots share the same position. We investigate the scattering problem in the limited-visibility model. In particular, we focus on

connectivity-preservation

property. That is, the scattering must be achieved so that the disconnection of the visibility graph never occurs (in the visibility graph robots are the nodes of the graph and the edges are their visibility relationship). The algorithm we propose assumes ATOM (

i.e.

semi-synchronous) model. In these settings our algorithm guarantees the connectivity-preserving property, and reaches a scattered configuration within

O

( min {

n

,

D

2

 + log

n

}) asynchronous rounds in expectation, where

D

is the diameter of the initial visibility graph. Note that the complexity analysis is

adaptive

since it depends on

D

. This implies that our algorithm quickly scatters all robots crowded in a small-diameter visibility graph. We also provide a lower bound of Ω(

n

) for connectivity-preserving scattering. It follows that our algorithm is optimal in the sense of the non-adaptive analysis.