A Fast Max Flow Algorithm

In 2013, Orlin proved that the max flow problem could be solved in $O(nm)$ time. His algorithm ran in $O(nm + m^{1.94})$ time, which was the fastest for graphs with fewer than $n^{1.06}$ arcs. If the graph was not sufficiently sparse, the fastest running time was an algorithm due to King, Rao, and Tarjan. We … Read more

An O(nm) time algorithm for finding the min length directed cycle in a graph

In this paper, we introduce an $O(nm)$ time algorithm to determine the minimum length directed cycle in a directed network with $n$ nodes and $m$ arcs and with no negative length directed cycles. This result improves upon the previous best time bound of $O(nm + n^2 \log\log n)$. Our algorithm first determines the cycle with … Read more

A Characterization of Irreducible Infeasible Subsystems in Flow Networks

Infeasible network flow problems with supplies and demands can be characterized via violated cut-inequalities of the classical Gale-Hoffman theorem. Written as a linear program, irreducible infeasible subsystems (IISs) provide a different means of infeasibility characterization. In this article, we answer a question left open in the literature, by showing a one-to-one correspondence between IISs and … Read more

Fully Polynomial Time Approximation Schemes for Stochastic Dynamic Programs

We present a framework for obtaining Fully Polynomial Time Approximation Schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone single-period cost functions. This framework is developed through the establishment of two sets of computational rules, namely the Calculus of K-approximation Functions and the Calculus of K-approximation Sets. Using our framework, we provide … Read more