Structural Multi-Optimality in Edge Server Placement for MEC Networks

Abstract

Edge server placement in mobile edge computing (MEC) networks is typically treated as an optimization problem with a unique solution. This paper shows that dense base station (BS) deployments produce multiple placements with identical cost, a phenomenon termed structural multi-optimality. A formal coverage-equivalence condition identifies when two BSs are interchangeable, and combinatorial bounds quantify the resulting solution multiplicity. Experiments on eight real BS datasets spanning three continents confirm that multi-optimality persists across four orders of magnitude of network density and is independent of the solver used. A demand-priority extension exploits this multiplicity by steering server selection toward high-demand BSs without increasing the server count. These results reframe MEC placement from a single-solution search into a landscape navigation problem, where planners can select among equivalent configurations to meet site-level and operational constraints.