Fast Deployment of UAV Networks for Optimal Wireless Coverage

Unmanned Aerial Vehicle (UAV) networks have emerged as a promising technique to rapidly provide wireless coverage to a geographical area, where a flying UAV can be fast deployed to serve as cell site. Existing work on UAV-enabled wireless networks overlook the fast UAV deployment for wireless coverage, and such deployment problems have only been studied recently in sensor networks. Unlike sensors, UAVs should be deployed to the air and they are generally different in flying speed, operating altitude and wireless coverage radius. By considering such UAV heterogeneity to cover the whole target area, this paper studies two fast UAV deployment problems: one is to minimize the maximum deployment delay among all UAVs (min-max) for fairness consideration, and the other is to minimize the total deployment delay (min-sum) for efficiency consideration. We prove both min-max and min-sum problems are NP-complete in general. When dispatching UAVs from the same location, we present an optimal algorithm of low computational complexity <inline-formula><tex-math notation="LaTeX">$O(n^2)$</tex-math><alternatives><inline-graphic xlink:href="zhang-ieq1-2840143.gif"/></alternatives></inline-formula> for the min-max problem. When UAVs are dispatched from different locations, we propose to preserve their location order during deployment and successfully design a fully polynomial time approximation scheme (FPTAS) of computation complexity <inline-formula><tex-math notation="LaTeX">$O(n^2 \log \frac{1}{\epsilon })$</tex-math><alternatives><inline-graphic xlink:href="zhang-ieq2-2840143.gif"/></alternatives></inline-formula> to arbitrarily approach the global optimum with relative error <inline-formula><tex-math notation="LaTeX">$\epsilon$</tex-math><alternatives><inline-graphic xlink:href="zhang-ieq3-2840143.gif"/></alternatives></inline-formula>. The min-sum problem is more challenging. When UAVs are dispatched from the same initial location, we present an approximation algorithm of linear time. As for the general case, we further reformulate it as a dynamic program and propose a pseudo polynomial-time algorithm to solve it optimally.