Flow Rounding

TL;DR

This paper introduces efficient algorithms for flow rounding problems, converting fractional flows into integral flows with minimal cost or randomized expected flow preservation, using cycle canceling techniques.

Contribution

It develops an $O(m \log(n^2/m))$ cycle canceling algorithm to solve flow rounding, improving efficiency for costed and randomized flow rounding problems.

Findings

Efficient cycle canceling algorithm for flow rounding

Optimal complexity of $O(m \log(n^2/m))$

Applicable to both costed and randomized flow rounding

Abstract

We consider flow rounding: finding an integral flow from a fractional flow. Costed flow rounding asks that we find an integral flow with no worse cost. Randomized flow rounding requires we randomly find an integral flow such that the expected flow along each edge matches the fractional flow. Both problems are reduced to cycle canceling, for which we develop an $O(m \log(n^2/m))$ algorithm.