An Improved Quasi-Physical Dynamic Algorithm for Efficient Circular Coverage in Arbitrary Convex

TL;DR

This paper introduces an Improved Quasi-Physical Dynamic algorithm that enhances circle coverage in arbitrary convex polygons by combining structure-preserving initialization, virtual force fields, and boundary management, outperforming existing methods.

Contribution

The paper presents a novel IQPD algorithm with a new initialization, force-based optimization, and boundary handling, improving coverage efficiency in complex convex polygons.

Findings

Significantly outperforms four state-of-the-art methods on seven metrics.

Effective in handling irregular convex polygons with high coverage efficiency.

Provides a practical solution for operational optimization and resource allocation.

Abstract

The optimal circle coverage problem aims to find a configuration of circles that maximizes the covered area within a given region. Although theoretical optimal solutions exist for simple cases, the problem's NP-hard characteristic makes the problem computationally intractable for complex polygons with numerous circles. Prevailing methods are largely confined to regular domains, while the few algorithms designed for irregular polygons suffer from poor initialization, unmanaged boundary effects, and excessive overlap among circles, resulting in low coverage efficiency. Consequently, we propose an Improved Quasi-Physical Dynamic(IQPD) algorithm for arbitrary convex polygons. Our core contributions are threefold: (1) proposing a structure-preserving initialization strategy that maps a hexagonal close-packing of circles into the target polygon via scaling and affine transformation; (2) constructing a virtual force field incorporating friction and a radius-expansion optimization iteration model; (3) designing a boundary-surrounding strategy based on normal and tangential gradients to retrieve overflowing circles. Experimental results demonstrate that our algorithm significantly outperforms four state-of-the-art methods on seven metrics across a variety of convex polygons. This work could provide a more efficient solution for operational optimization or resource allocation in practical applications.