Optimal Perimeter Guarding with Heterogeneous Robot Teams: Complexity Analysis and Effective Algorithms

TL;DR

This paper studies the complexity of optimal perimeter guarding with heterogeneous robots, proving intractability for some cases and developing scalable algorithms for practical scenarios, validated by extensive experiments.

Contribution

It introduces generalized versions of the perimeter guarding problem with heterogeneous robots, analyzes their computational complexity, and proposes effective algorithms for practical cases.

Findings

OPG_LR is strongly NP-hard.

Pseudo-polynomial algorithms are effective for fixed-parameter cases.

Algorithms are validated through extensive numerical experiments.

Abstract

We perform structural and algorithmic studies of significantly generalized versions of the optimal perimeter guarding (OPG) problem. As compared with the original OPG where robots are uniform, in this paper, many mobile robots with heterogeneous sensing capabilities are to be deployed to optimally guard a set of one-dimensional segments. Two complimentary formulations are investigated where one limits the number of available robots (OPG_LR) and the other seeks to minimize the total deployment cost (OPG_MC). In contrast to the original OPG which admits low-polynomial time solutions, both OPG_LR and OPG_MC are computationally intractable with OPG_LR being strongly NP-hard. Nevertheless, we develop fairly scalable pseudo-polynomial time algorithms for practical, fixed-parameter subcase of OPG_LR; we also develop pseudo-polynomial time algorithm for general OPG_MC and polynomial time algorithm for the fixed-parameter OPG_MC case. The applicability and effectiveness of selected algorithms are demonstrated through extensive numerical experiments.