Gathering over Meeting Nodes in Infinite Grid

TL;DR

This paper addresses the problem of robots gathering at designated meeting nodes on an infinite grid, providing a deterministic algorithm and analyzing its efficiency and move complexity.

Contribution

It characterizes initial configurations where gathering is impossible and proposes a deterministic solution for the rest, along with efficiency analysis and move lower bounds.

Findings

Characterized initial configurations with deterministic gathering impossibility.

Proposed a deterministic algorithm for solvable configurations.

Derived a lower bound on total moves required for gathering.

Abstract

The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. Robots are identical, autonomous, anonymous and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on a global coordinate system. All the initial configurations for which the problem is deterministically unsolvable have been characterized. A deterministic distributed algorithm has been proposed to solve the problem for the remaining configurations. The efficiency of the proposed algorithm is studied in terms of the number of moves required for gathering. A lower bound concerning the total number of moves required to solve the gathering problem has been derived.