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In this paper, we consider time-dependent networks, and the task of computing cost-optimal paths, which are constrained to stay close to fastest paths. We derive pruning criteria, which significantly improve both the number of vertex-time pairs expanded during search and the memory required to ensure the correctness of any solution algorithm. We then prove new complexity results, which imply that the problem of computing constrained cost-optimal paths in a discrete-time setting is polynomiallydoi:10.7155/jgaa.00201 fatcat:3zxxejex65euvgz3kdhgtfezni