A Faster Algorithm for Packing Branchings in Digraphs

TL;DR

This paper introduces a more efficient algorithm for packing branchings in capacitated digraphs with root-set demands, reducing the number of branchings and oracle calls compared to previous methods.

Contribution

The authors present a faster algorithm that improves the bounds on branchings and oracle calls for packing branchings in digraphs with demands.

Findings

Returns a packing with at most m+r-1 branchings

Reduces oracle calls to at most 2n+m+r-1

Improves efficiency over Schrijver's algorithm

Abstract

We consider the problem of finding an integral packing of branchings in a capacitated digraph with root-set demands. Schrijver described an algorithm that returns a packing with at most m+n^3+r branchings that makes at most m(m+n^3+r) calls to an oracle that basically computes a minimum cut, where n is the number of vertices, m is the number of arcs and r is the number of root-sets of the input digraph. In this work we provide an algorithm, inspired on ideas of Schrijver and on an paper of Gabow and Manu, that returns a packing with at most m+r-1 branchings and makes at most 2n+m+r-1 oracle calls.