A Polynomial Combinatorial Algorithm for Generalized Minimum Cost Flow

A Faster Strongly Polynomial Minimum Cost Flow Algorithm

In this paper, we present a new strongly polynomial time algorithm for the minimum cost flow problem, based on a refinement of the Edmonds-Karp scaling technique. Our algorithm solves the uncapacitated minimum cost flow problem as a sequence of O(n log n) shortest path problems on networks with n nodes and m arcs and runs in O(n log n (m + n log n)) time. Using a standard transformation, thjis ...

A strongly polynomial minimum cost circulation algorithm

Strongly polynomial algorithm for generalized flow maximization

A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of steps, an arc can be identified that must be tight in every dual optimal solution, and thus can be contracted. The full version is available on arXiv:1307.680...

A polynomial-time algorithm for a class of minimum concave cost flow problems

We study the minimum concave cost flow problem over a two-dimensional grid network (CFG), where one dimension represents time (1 ≤ t ≤ T ) and the other dimension represents echelons (1 ≤ l ≤ L). The concave function over each arc is given by a value oracle. We give a polynomial-time algorithm for finding the optimal solution when the network has a fixed number of echelons and all sources lie a...

An Implementation of a Combinatorial Approximation Algorithm for Minimum-Cost Multicommodity Flow

Theminimum-cost multicommodity ow problem involves simultaneously shipping multiple commodities through a single network so that the total ow obeys arc capacity constraints and has minimum cost. Multicommodity ow problems can be expressed as linear programs, and most theoretical and practical algorithms use linear-programming algorithms specialized for the problems' structures. Combinatorial ap...