Online Drone Coverage of Targets on a Line

TL;DR

This paper investigates online algorithms for drone coverage of targets on a line, optimizing trajectory length with competitive ratio bounds for different camera angles.

Contribution

It introduces three online algorithms with proven competitive ratios and establishes a lower bound, advancing understanding of online drone coverage strategies.

Findings

The extsc{FA} algorithm has a competitive ratio of 1.25 at b1= b1/4.

b7b7b7

Lower bound on competitive ratio is approximately 1.207 at b1= b1/4.

Abstract

We study a problem of online targets coverage by a drone or a sensor that is equipped with a camera or an antenna of fixed half-angle of view $\alpha$. The targets to be monitored appear at arbitrary positions on a line barrier in an online manner. When a new target appears, the drone has to move to a location that covers the newly arrived target, as well as already existing targets. The objective is to design a coverage algorithm that optimizes the total length of the drone's trajectory. Our results are reported in terms of an algorithm's competitive ratio, i.e., the worst-case ratio (over all inputs) of its cost to that of an optimal offline algorithm. In terms of upper bounds, we present three online algorithms and prove bounds on their competitive ratios for every $\alpha \in [0, \pi/2]$. The best of them, called \FA is significantly better than the other two for $\pi/6 < \alpha < \pi/3$. In particular, for $\alpha=\pi/4$, its worst case, \FA has competitive ratio $1.25$, while the other two have competitive ratio $\sqrt{2}$. Finally, we prove a lower bound on the competitive ratio of online algorithms for a drone with half-angle $\alpha \in [0, \pi/4]$; this bound is a function of $\alpha$ that achieves its maximum value at $\alpha = \pi/4$ equal to $(1+\sqrt{2})/2 \approx 1.207$.