Randomized Parallel Approximations to Max Flow

Years and Authors of Summarized Original Work

• 1991; Serna, Spirakis

Problem Definition

The work of Serna and Spirakis provides a parallel approximation schema for the Maximum Flow problem. An approximate algorithm provides a solution whose cost is within a factor of the optimal solution. The notation and definitions are the standard ones for networks and flows (see for example [2, 7]).

A network${ N=(G,s,t,c)}$ is a structure consisting of a directed graph ${ G=(V,E) }$, two distinguished vertices, ${ s,t\in V}$ (called the source and the sink), and ${c:E\rightarrow \mathbb{Z}^+}$, an assignment of an integer capacity to each edge in E. A flow functionf is an assignment of a non-negative number to each edge of G (called the flow into the edge) such that first at no edge does the flow exceed the capacity, and second for every vertex except s and t, the sum of the flows on its incoming edges equals the sum of the flows on its outgoing edges. The total flowof a given flow...