arXiv subjects

Zeping Yi

Publications and source records attributed to Zeping Yi.

3 recordsLinked to original sources

arXiv2026

A fast improved quasi-physical dynamic algorithm for efficient wireless coverage in convex polygonal regions

Deploying wireless nodes to maximize coverage area within a given region is an important challenge in wireless sensor networks, UAV path planning, base station placement and other industrial fields. This practical problem can be mathematically equivalent to an optimal circle covering problem. Although theoretical optimal configurations exist for simple cases in mathematics, the NP-hard nature of this problem makes it computationally prohibitive for complex polygons with numerous nodes. Existing approaches are usually designed for regular domains, while those applicable to irregular polygons often suffer from poor initialization, excessive coverage overlap and failure to constrain nodes within the boundary, leading to low coverage efficiency and long runtime. To address these issues, we propose an improved quasi-physical dynamic algorithm (IQPD) for wireless node deployment in arbitrary convex polygons. Our contributions are threefold: (1) proposing a structure-preserving initialization that maps a hexagonal close packing pattern into the target polygon via scaling and affine transformation, ensuring near-optimal initial node distribution; (2) constructing a refined virtual force model by incorporating friction and a radius-expansion optimization mechanism to reduce coverage area overlap; (3) developing a boundary encircling strategy leveraging normal and tangential gradients to reposition nodes deployed outside boundaries after initial optimization. Extensive experimental results demonstrate that our method consistently outperforms other new metaheuristic algorithms across diverse convex polygon shapes, including randomly generated data and real-world scenarios. Our method achieves the highest coverage rate and node utilization rate among all compared algorithms, greatly improving wireless coverage efficiency.

cs.CG↗

arXiv2026

An improved boundary-focused adaptive quadtree algorithm for circle-polygon intersection area approximation

In this paper, we present an improved numerical algorithm for computing the intersection area of multiple circles and a complex polygon efficiently. This geometric problem is fundamental to applications such as wireless sensor networks and base station deployment. The key idea is a curvature-multiplicity-guided adaptive sampling strategy that dynamically concentrates sampling points in geometrically complex boundary regions. The algorithm integrates three components: (i) adaptive quadtree partitioning, (ii) analytical integration via Green's theorem for cells intersecting a single circle, and (iii) curvature-multiplicity-guided Monte Carlo subsampling for cells intersecting multiple circles, where a minimum sample count and a constant factor are introduced into the sampling size. Theoretical analysis shows that the algorithm achieves O(1/{\epsilon}3/2) computational complexity while maintaining an O({\epsilon}) error bound, improving upon the O(1/{\epsilon}2) complexity of classical Monte Carlo and uniform grid methods for the same error tolerance {\epsilon}. Numerical experiments on complex polygons, including synthetic data and real-world scenarios, demonstrate that our algorithm outperforms five classical methods in terms of relative error. Furthermore, parameter sensitivity analysis confirms that the algorithm is robust and could make it suited for practical applications such as wireless sensor network coverage estimation.

cs.CG↗

arXiv2026

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

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.

cs.CG↗