Minimal networks for sensor counting problem using discrete Euler calculus

TL;DR

This paper introduces a novel method leveraging discrete Euler calculus to reduce noise and improve target enumeration accuracy in acyclic sensor networks, enhancing reliability and optimization.

Contribution

It presents a new approach to identify reducible points in acyclic sensor networks using discrete Euler calculus, generalizing weak beat points for better noise reduction.

Findings

Effective noise reduction in sensor networks

Improved target enumeration accuracy

Enhanced network reliability and optimization

Abstract

This paper proposes a method to reduce noise in acyclic sensor networks enumerating targets using the integral theory with respect to Euler characteristic. For an acyclic network (a partially ordered set) equipped with sensors detecting targets, we find reducible points for enumerating targets, as a generalization of weak beat points (homotopically reducible points). This theory is useful for improving the reliability and optimization of acyclic sensor networks.