Improved Approximations for Guarding 1.5-Dimensional Terrains

TL;DR

This paper introduces a 4-approximation algorithm for guarding 1.5D terrains, improving the previous best factor of 5, and extends to weighted and partial guarding problems using LP relaxation techniques.

Contribution

It presents a simpler, more effective approximation algorithm that generalizes to weighted and partial guarding scenarios, advancing prior methods.

Findings

Achieved a 4-approximation factor, better than previous 5-approximation.

The LP rounding approach simplifies analysis and implementation.

The method extends to weighted and partial guarding problems.

Abstract

We present a 4-approximation algorithm for the problem of placing a fewest guards on a 1.5D terrain so that every point of the terrain is seen by at least one guard. This improves on the currently best approximation factor of 5. Our method is based on rounding the linear programming relaxation of the corresponding covering problem. Besides the simplicity of the analysis, which mainly relies on decomposing the constraint matrix of the LP into totally balanced matrices, our algorithm, unlike previous work, generalizes to the weighted and partial versions of the basic problem.