Abstract
We study an extension of the well-known generalized maximum flow problem in which the outflow of an edge is a strictly increasing convex function of its inflow. In contrast to the traditional generalized maximum flow problem, in which the outflow of an edge depends linearly on its inflow and which is solvable in polynomial time, we show that, for convex outflow functions, the problem becomes strongly NP-hard to solve even on bipartite acyclic graphs and weakly NP-hard on series–parallel graphs. Both results hold even if the outflow functions are convex quadratic. Furthermore, we present (exponential-time) exact algorithms for computing optimal flows on acyclic and series–parallel graphs and optimal preflows on general graphs. We also show that a flow decomposition similar to the one for traditional generalized flows is possible and present a pseudo-polynomial-time algorithm for the case of integral flows on series–parallel graphs.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
