In this article, we address the problem of synthesizing UAV communication networks in the presence of resource constraints. UAVs can be deployed as backbone nodes in ad-hoc networks that can be central to civilian and military applications. The cost of operation of the network depends on the resources that are used such as the total power consumption associated with the network and the number of communication links in the network. The objective of the problem is to synthesize a communication network that maximizes connectivity subject to cost of operation being within the specified resource. We choose algebraic connectivity as a measure of connectivity of the network as it is known to be a measure of robust connectivity to random node failures in the network. We pose the network synthesis problem as a mixed-integer semi-definite program and provide (1) an algorithm for computing optimal solutions using cutting plane methods, and (2) construct feasible solutions using heuristics and estimate their quality. The network synthesis problem is a NP-hard problem and there are no guarantees on the running time of the algorithm that computes an optimal solution. We provide some computational results to corroborate the performance of the proposed algorithms.

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