Approximation Algorithms for Anchored Multiwatchman Routes

TL;DR

This paper introduces the first tight approximation algorithms for the anchored multi-watchman routes problem in polygons, providing an FPTAS for fixed k and constant-factor approximations when k varies.

Contribution

It presents the first tight approximability results for the multi-watchman routes problem, including an FPTAS for fixed k and constant-factor approximations for variable k.

Findings

FPTAS developed for fixed number of watchmen

Constant-factor approximations for variable number of watchmen

Dynamic programming algorithm underpins the FPTAS

Abstract

We study some variants of the $k$-\textsc{Watchman Routes} problem, the cooperative version of the classic \textsc{Watchman Routes} problem in a simple polygon. The watchmen may be required to see the whole polygon, or some pre-determined quota of area within the polygon, and we want to minimize the maximum length traveled by any watchman. While the single watchman version of the problem has received much attention is rather well understood, it is not the case for multiple watchmen version. We provide the first tight approximability results for the anchored $k$-\textsc{Watchman Routes} problem in a simple polygon, assuming $k$ is fixed, by a fully-polynomial time approximation scheme. The basis for the FPTAS is provided by an exact dynamic programming algorithm. If $k$ is a variable, we give constant-factor approximations.