Relay Positioning for Unmanned Aerial Vehicle Surveillance ∗ Oleg Burdakov ⋆ , Patrick Doherty † , Kaj Holmberg ⋆ ,JonasKvarnstr¨om † , Per-Magnus Olsson †,‡ ⋆ Dept. of Mathematics. E-mail: {olbur, kahol}@mai.liu.se † Dept. of Computer and Information Science. E-mail: {pdy, jonkv, perol}@ida.liu.se Link¨ oping University, SE-581 83 Link¨ oping, Sweden ‡ Corresponding author Abstract When unmanned aerial vehicles (UAVs) are used for surveillance, infor- mation must often be transmitted to a base station in real time. However, limited communication ranges and the common requirement of free line of sight may make direct transmissions from distant targets impossible. This problem can be solved using relay chains consisting of one or more intermediate relay UAVs. This leads to the problem of positioning such relays given known obstacles, while taking into account a possibly mission- specific quality measure. The maximum quality of a chain may depend strongly on the number of UAVs allocated. Therefore, it is desirable to either generate a chain of maximum quality given the available UAVs or allow a choice from a spectrum of Pareto-optimal chains corresponding to different trade-offs between the number of UAVs used and the resulting quality. In this article, we define several problem variations in a continuous 3D setting. We show how sets of Pareto-optimal chains can be generated using graph search and present a new label-correcting algorithm generating such chains significantly more efficiently than the best known algorithms in the literature. Finally, we present a new dual ascent algorithm with better performance for certain tasks and situations. 1 Introduction A wide variety of applications of unmanned aerial vehicles (UAVs) include the need for surveillance of distant targets, including search and rescue operations, traffic surveillance and forest fire monitoring as well as law enforcement and military applications. In many cases, the information gathered by a surveil- lance UAV must be transmitted in real time to a base station where the current operation is being coordinated. This information often includes live video feeds, ∗ This is an extended version of Burdakov et al. (2009a). 1