3 Minimum cost network flow problem 5 3.1 Transportation problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 The maximum flow problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3 The shortest path problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.4 The single source shortest paths . . . . . . . . . . . . . . . . ...

D. Ray Fulkerson (1922–1976) made fundamental and lasting contributions to combinatorial mathematics, optimization, and operations research [2]. He is probably best known for his work on network flows and in particular for the famous max flow–min cut theorem, stating that the maximum amount of a flow from a node s to a node t in a directed graph equals the minimum capacity of a cut separating s...

In this paper, we consider the inverse spanning tree problem. Given an undirected graph Go = (Ni, AO) with n nodes, mn arcs, an arc cost vector c, and a spanning tree T, the inverse spanning tree problem is to perturb the arc cost vector c to a vector d so that T is a minimum spanning tree with respect to the cost vector d and the cost of perturbation given by Id c = L(l j) Aldij ciil is minimu...

We introduce polylinking networks, which is a flow model based on polylinking systems that generalizes the classical flow model of Ford and Fulkerson on acyclic networks and has applications in the context of wireless networks. More precisely, a flow model recently introduced by Avestimehr et al. (Proceedings of the Allerton conference on communication, control, and computing 2007) used in the ...

Physarum polycephalum (true slime mold) has recently emerged as a fascinating example of biological computation through morphogenesis. Despite being a single cell organism, experiments have observed that through its growth process, the Physarum is able to solve various minimum cost flow problems. This paper analyzes a mathematical model of the Physarum growth dynamics. We show how to encode gen...

This report provides an (updated) overview of Grafalgo, an opensource library of graph algorithms and the data structures used to implement them. The programs in this library were originally written to support a graduate class in advanced data structures and algorithms at Washington University. Because the code’s primary purpose was pedagogical, it was written to be as straightforward as possib...