Conflicting Bundle Allocation with Preferences in Weighted Directed Acyclic Graphs: Application to Orbit Slot Allocation Problems

We introduce resource allocation techniques for problems where (i) the agents express requests for obtaining item bundles as compact edge-weighted directed acyclic graphs (each path in such a graph is a bundle whose valuation is the sum of the weights of the traversed edges), and (ii) the agents do not bid on the exact same items but may bid on conflicting items that cannot be both assigned or that require accessing a specific resource with limited capacity. This setting is motivated by real applications such as Earth observation slot allocation, virtual network functions, or multi-agent path finding. We model several directed path allocation problems (vertex-constrained and resource-constrained), investigate several solution methods (qualified as exact or approximate, and utilitarian or fair), and analyze their performances on an orbit slot ownership problem, for realistic requests and constellation configurations.