Reconfiguration of Squares Using a Constant Number of Moves Each

TL;DR

This paper studies a constrained multi-robot motion planning problem involving square robots that can only slide a limited number of times, revealing its computational complexity and identifying special cases where the problem is easier.

Contribution

The paper introduces a restricted variant of multi-robot motion planning with limited moves per square and characterizes its NP-hardness, highlighting cases with unit-sized squares and unlabeled targets as exceptions.

Findings

The problem remains NP-hard in most cases.

Unit-sized squares with unlabeled targets allow polynomial solutions.

Abstract

Multi-robot motion planning is a hard problem. We investigate restricted variants of the problem where square robots are allowed to slide over an arbitrary curve to a new position only a constant number of times each. We show that the problem remains NP-hard in most cases, except when the squares have unit size and when the problem is unlabeled, i.e., the location of each square in the target configuration is left unspecified.