Minimum Flows in Directed 1−n Planar Static and Dynamic Networks with Arcs and Nodes Capacities

Abstract

Planar networks are an important special class of networks that arise in several application contexts. Because of the special structure of planar networks, network flow algorithms often run faster on these networks than they do on more general networks. In first part (Secs. 2–5), we present an algorithm for finding maximum cut and an algorithm for finding minimum flow in directed [Formula: see text] planar static networks with arcs and nodes capacities. This part is presented in Ciurea et al. [Proc. 5th Int. Conf. Control Decision and Information Technologies (CoDIT2018), Thessaloniki, Greece (2018), pp. 110–115]. In the second part (Secs. 6–8), we present this problem in directed [Formula: see text] planar dynamic networks with arcs and nodes capacities.