The NP-completeness of Redundant Open-Locating-Dominating Set

TL;DR

This paper proves that finding a minimal redundant open-locating-dominating set in a graph is an NP-complete problem, highlighting computational complexity challenges in sensor placement for detection systems.

Contribution

It establishes the NP-completeness of the redundant OLD set problem, a variant important for sensor network design and fault detection.

Findings

Proves NP-completeness of the redundant OLD set problem

Highlights computational difficulty in sensor placement optimization

Provides theoretical foundation for future algorithm development

Abstract

For a graph G, a dominating set D is a subset of vertices in G where each of the vertices in G is in D or adjacent to some vertex in D. An open-locating-dominating (OLD) set models a system with sensors to detect an intruder in a facility or a faulty component in a network of processors. The goal is to detect and pinpoint an intruder's exact location in a system with a minimum number of sensors. In this paper, we focus on a variant of an OLD set called a redundant OLD set and present a proof for the NP-completeness of the problem of a redundant OLD set.