An Asynchronous Maximum Independent Set Algorithm by Myopic Luminous Robots on Grids

TL;DR

This paper presents two algorithms for mobile luminous robots to construct a maximum independent set on finite grid networks, with different assumptions on robot capabilities and network knowledge, achieving efficient movement bounds.

Contribution

It introduces two novel distributed algorithms for asynchronous luminous robots to form maximum independent sets on grids, relaxing assumptions step-by-step.

Findings

First algorithm uses 3 light colors, range 2, with port-numbering.

Second algorithm uses 7 light colors, range 3, removing port-numbering.

Both algorithms have movement complexity of O(n(L+l)).

Abstract

We consider the problem of constructing a maximum independent set with mobile myopic luminous robots on a grid network whose size is finite but unknown to the robots. In this setting, the robots enter the grid network one-by-one from a corner of the grid, and they eventually have to be disseminated on the grid nodes so that the occupied positions form a maximum independent set of the network. We assume that robots are asynchronous, anonymous, silent, and they execute the same distributed algorithm. In this paper, we propose two algorithms: The first one assumes the number of light colors of each robot is three and the visible range is two, but uses additional strong assumptions of port-numbering for each node. To delete this assumption, the second one assumes the number of light colors of each robot is seven and the visible range is three. In both algorithms, the number of movements is $O(n(L+l))$ steps where $n$ is the number of nodes and $L$ and $l$ are the grid dimensions.