A New Lower Bound on Guard Placement for Wireless Localization

TL;DR

This paper establishes a new lower bound of approximately 2n/3 stations needed for wireless localization with vertex-restricted stations, improving previous bounds and advancing understanding of minimal station placement.

Contribution

It introduces a tighter lower bound for station placement in wireless localization when stations are restricted to polygon vertices.

Findings

Lower bound of 2n/3 - 1 stations for general position polygons

Improvement over previous n/2 lower bound

Enhanced understanding of minimal station requirements

Abstract

The problem of wireless localization asks to place and orient stations in the plane, each of which broadcasts a unique key within a fixed angular range, so that each point in the plane can determine whether it is inside or outside a given polygonal region. The primary goal is to minimize the number of stations. In this paper we establish a lower bound of 2n/3 - 1 stations for polygons in general position, for the case in which the placement of stations is restricted to polygon vertices, improving upon the existing n/2 lower bound.