A Fast 2-Approximation Algorithm for Guarding Orthogonal Terrains

TL;DR

This paper presents a faster 2-approximation algorithm for the NP-complete Terrain Guarding Problem on 1.5D orthogonal terrains, reducing the running time from quadratic to near-linear.

Contribution

The authors develop a more efficient 2-approximation algorithm for TGP on orthogonal terrains with improved runtime complexity.

Findings

Achieved a 2-approximation with O(n log m) time

Improved upon previous O(n^2) algorithm

Applicable to 1.5D orthogonal terrains

Abstract

Terrain Guarding Problem(TGP), which is known to be NP-complete, asks to find a smallest set of guard locations on a terrain $T$ such that every point on $T$ is visible by a guard. Here, we study this problem on 1.5D orthogonal terrains where the edges are bound to be horizontal or vertical. We propose a 2-approximation algorithm that runs in O($n \log m$) time, where $n$ and $m$ are the sizes of input and output, respectively. This is an improvement over the previous best algorithm, which is a 2-approximation with O($n^2$) running time.