Coarse Differentiation and Multi-flows in Planar Graphs

Coarse Differentiation and Multi-flows in Planar Graphs

We show that the multi-commodity max-flow/min-cut gap for series-parallel graphs can be as bad as 2, matching a recent upper bound [8] for this class, and resolving one side of a conjecture of Gupta, Newman, Rabinovich, and Sinclair. This also improves the largest known gap for planar graphs from 32 to 2, yielding the first lower bound that doesn’t follow from elementary calculations. Our appro...

Boundary-to-Boundary Flows in Planar Graphs

We give an iterative algorithm for finding the maximum flow between a set of sources and sinks that lie on the boundary of a planar graph. Our algorithm uses only O(n) queries to simple data structures, achieving an O(n logn) running time that we expect to be practical given the use of simple primitives. The only existing algorithm for this problem uses divide and conquer and, in order to achie...

Improved Minimum Cuts and Maximum Flows in Undirected Planar Graphs

In this paper we study minimum cut and maximum flow problems on planar graphs, both in static and in dynamic settings. First, we present an algorithm that given an undirected planar graph computes the minimum cut between any two given vertices in O(n log logn) time. Second, we show how to achieve the same O(n log logn) bound for the problem of computing maximum flows in undirected planar graphs...

Antisymmetric flows and strong oriented coloring of planar graphs

Comparison of Binomial and Power Equations in Radial Non-Darcy Flows in Coarse Porous Media

Analysis of non-laminar flows in coarse alluvial beds has a wide range of applications in various civil engineering, oil and gas, and geology problems. Darcy equation is not valid to analyze transient and turbulent flows, so non-linear equations should be applied. Non-linear equations are classified into power and binomial equations. Binomial equation is more accurate in a wide range of velocit...