arXiv subjects

C. Nahak

Publications and source records attributed to C. Nahak.

5 recordsLinked to original sources

arXiv2026

On $\phi$-Best Proximity Points and Proximal-type Algorithms in Banach Spaces

The purpose of this paper is to study the existence and convergence of $\phi$-best proximity points in Banach spaces. A strong convergence theorem is established by employing a shrinking projection algorithm designed to compute common $\phi$-best proximity points of a proximally weakly suppressive mapping. Finally, we address a projection scheme to solve split $\phi$-best proximity point and variational problem in a Banach space. These contributions provide new tools for solving nonlinear problems involving non-self mappings.

math.FA↗

arXiv2026

Robust priority-aware coverage optimization for aerial sensor networks

This article presents a priority-aware robust coverage optimization framework for an aerial sensor network under sensor location uncertainty. Each region is assigned a priority weight, and the objective is to maximize the weighted coverage while maintaining robustness against positional perturbations. A mathematical optimization model is developed by incorporating surveillance constraints and an RRF-based robustness formulation into the proposed framework. An efficient priority-aware robust orientation optimization (PAROO) algorithm is then proposed to determine the sensor orientations that maximize the weighted coverage objective. Experimental results on an airport-inspired surveillance scenario demonstrate that the proposed framework effectively directs sensing resources toward high-priority regions and achieves higher weighted coverage than representative baseline approaches, highlighting its practical applicability in security-sensitive environments.

math.OC↗

arXiv2026

Robust sensor coverage in the presence of spatial obstacles and exclusion zones

In this article, we develop a robust optimization framework for obstacle-aware aerial directional sensor networks operating under positional uncertainty using a sector-based sensing model. The monitoring area is discretized into grid points and a unified geometric formulation is developed to model directional sensing while explicitly accounting for obstacle-induced visibility loss and exclusion regions. To enhance sensing performance under uncertainty, three progressive optimization strategies, namely robust aerial grid coverage (RAGC), robust aerial target coverage (RATC) and robust aerial target scheduling (RATS), are proposed. The framework employs robust orientation optimization based on the radius of robust feasibility to maximize effective grid and target coverage under sensor perturbations, followed by a target-aware sleep scheduling mechanism that minimizes the number of active sensors without compromising target monitoring. Extensive simulations under varying target distributions, obstacle configurations, uncertainty levels and sensor failure scenarios demonstrate that the proposed framework achieves robust and energy-efficient sensing while consistently outperforming representative approaches from the literature in terms of coverage quality, target monitoring and sensor utilization.

math.OC↗

arXiv2025

Robust Optimization Framework for Ground Coverage in Aerial Sensor Networks

Sensors play a critical role in environmental monitoring, but their coverage performance degrades significantly under spatial uncertainty. This article proposes a robust optimization framework for maximizing ground coverage in aerial directional sensor networks subject to sensor displacement. Each aerial sensor projects a truncated sector on the ground, parameterized by its altitude, field of view, and orientation. To explicitly capture robustness against positional uncertainty, we adopt the radius of robust feasibility (RRF) as a quantitative measure of tolerance to worst-case perturbations. The RRF formulation for aerial sensor networks is embedded directly into the coverage maximization problem, ensuring feasibility under bounded uncertainty. The resulting worst-case coverage problem is nonconvex and NP-hard; therefore, a distributed greedy orientation algorithm based on Voronoi partitioning is applied to adjust sensor orientations using only local information, while directing coverage toward high-impact regions. Simulation results demonstrate that the proposed method consistently preserves robust coverage across complex terrain, varying parameters and uncertain operating conditions, highlighting its practical significance for aerial sensing applications.

math.OC↗

arXiv2025

A Radius of Robust Feasibility Approach to Directional Sensors in Uncertain Terrain

A sensor has the ability to probe its surroundings. However, uncertainties in its exact location can significantly compromise its sensing performance. The radius of robust feasibility defines the maximum range within which robust feasibility is ensured. This work introduces a novel approach integrating it with the directional sensor networks to enhance coverage using a distributed greedy algorithm. In particular, we provide an exact formula for the radius of robust feasibility of sensors in a directional sensor network. The proposed model strategically orients the sensors in regions with high coverage potential, accounting for robustness in the face of uncertainty. We analyze the algorithm's adaptability in dynamic environments, demonstrating its ability to enhance efficiency and robustness. Experimental results validate its efficacy in maximizing coverage and optimizing sensor orientations, highlighting its practical advantages for real-world scenarios.

math.OC↗