Optimum Flows in Directed Planar Dynamic Networks. The Dynamic Approch

Abstract

Optimum flows in directed planar dynamic networks are essential for several reasons, impacting a varietyof fields. These networks present unique challenges that require advanced optimization techniques to ensure efficient andreliable performance. In this paper we consider a time-varying directed planar network without parallel arcs and loops,where a flow must take a certain time to traverse an arc. The problem is to find an optimal (minimal or maximal) solutionto send the optimum (minimum or maximum) flow from the source node to the sink node, within a given timeT.