Polynomial time minimum cost path algorithms for acyclic networks of C-depth bridges with piece-wise linear time-varying travel costs and transit delays

Minimum cost path problems are considered for time-varying networks which possess piecewise linear travel costs/transit delays on edges and constant parking costs/enterable-unenterable restrictions on nodes. The arrival characteristics and departure characteristics are formulated, and their computation algorithms are designed. These characteristics are not values but curves with respect to generic time, which are novel features contrasted with the conventional time-invariant problems. Piecewise linearity of costs and delays drastically reduces the computational complexity