# Competitive Perimeter Defense of Conical Environments

arXiv: https://arxiv.org/abs/2110.04667 · HTML: https://mlsanity.com/paper/2110.04667/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2021.

## Built on by (most cited first, 3 of 3)

- [Graph Neural Networks for Decentralized Multi-Agent Perimeter Defense](https://mlsanity.com/paper/2301.09689/) (2023)
- [A Decentralized Spike-based Learning Framework for Sequential Capture in Discrete Perimeter Defense Problem](https://mlsanity.com/paper/2305.16748/) (2023)
- [Game-Theory-Assisted Reinforcement Learning for Border Defense: Early Termination based on Analytical Solutions](https://mlsanity.com/paper/2603.15907/) (2026)

## Abstract (arXiv)

We consider a perimeter defense problem in a planar conical environment in which a single vehicle, having a finite capture radius, aims to defend a concentric perimeter from mobile intruders. The intruders are arbitrarily released at the circumference of the environment and they move radially toward the perimeter with fixed speed. We present a competitive analysis approach to this problem by measuring the performance of multiple online algorithms for the vehicle against arbitrary inputs, relative to an optimal offline algorithm that has information about entire input sequence in advance. In particular, we establish two necessary conditions on the parameter space to guarantee (i) finite competitiveness of any algorithm and (ii) a competitive ratio of at least 2 for any algorithm. We then design and analyze three online algorithms and characterize parameter regimes in which they have finite competitive ratios. Specifically, our first two algorithms are provably 1, and 2-competitive, respectively, whereas our third algorithm exhibits different competitive ratios in different regimes of problem parameters. Finally, we provide a numerical plot in the parameter space to reveal additional insights into the relative performance of our algorithms.