Approximate offline optimization on arbitrary finite metrics

Determine whether route approximation can be combined with an endpoint-indexed schedule approximation for offline per-batch maximum-delay service on arbitrary finite metrics without compounding approximation errors across many service batches.

Background

Exact offline optimization is polynomial-time solvable on finite lines and explicitly represented weighted trees, but the paper proves NP-hardness on arbitrary finite metrics even when all requests arrive simultaneously. The authors therefore identify approximation, specifically the interaction between approximating individual routes and approximating the endpoint-dependent schedule, as the central unresolved computational issue.