Maximum Independent Set Formation on a Finite Grid by Myopic Robots

TL;DR

This paper presents a deterministic distributed algorithm enabling autonomous, anonymous robots with limited visibility to form a maximum independent set on a finite grid, even with arbitrary initial placement, under semi-synchronous scheduling.

Contribution

It introduces a novel algorithm for MIS formation that works with arbitrary initial robot placement, limited visibility, and minimal communication.

Findings

Algorithm guarantees MIS formation in finite time.

Works with robots placed arbitrarily on the grid.

Operates under semi-synchronous scheduler with minimal resources.

Abstract

This work deals with the Maximum Independent Set ($\mathcal{MIS}$) formation problem in a finite rectangular grid by autonomous robots. Suppose we are given a set of identical robots, where each robot is placed on a node of a finite rectangular grid $\mathcal{G}$ such that no two robots are on the same node. The $\mathcal{MIS}$ formation problem asks to design an algorithm, executing which each robot will move autonomously and terminate at a node such that after a finite time the set of nodes occupied by the robots is a maximum independent set of $\mathcal{G}$. We assume that robots are anonymous and silent, and they execute the same distributed algorithm. Previous works solving this problem used one or several door nodes through which the robots enter inside the grid or the graph one by one and occupy required nodes. In this work, we propose a deterministic algorithm that solves the $\mathcal{MIS}$ formation problem in a more generalized scenario, i.e., when the total number of required robots to form an $\mathcal{MIS}$ are arbitrarily placed on the grid. The proposed algorithm works under a semi-synchronous scheduler using robots with only 2 hop visibility range and only 3 colors.