Designing Multi-Commodity Flow Trees

TL;DR

This paper presents an approximation algorithm for designing multi-commodity flow networks as trees with constant degree, improving the approximation ratio by leveraging balanced-separator procedures.

Contribution

It introduces a novel approximation algorithm for multi-commodity flow network design as trees, reducing the problem to a balanced-separator problem with improved guarantees.

Findings

Performance guarantee within a factor of 4 of the balanced-separator's guarantee

Using Leighton and Rao's procedure yields an O(log n) guarantee

Improves previous O(log^2 n) approximation for the problem

Abstract

The traditional multi-commodity flow problem assumes a given flow network in which multiple commodities are to be maximally routed in response to given demands. This paper considers the multi-commodity flow network-design problem: given a set of multi-commodity flow demands, find a network subject to certain constraints such that the commodities can be maximally routed. This paper focuses on the case when the network is required to be a tree. The main result is an approximation algorithm for the case when the tree is required to be of constant degree. The algorithm reduces the problem to the minimum-weight balanced-separator problem; the performance guarantee of the algorithm is within a factor of 4 of the performance guarantee of the balanced-separator procedure. If Leighton and Rao's balanced-separator procedure is used, the performance guarantee is O(log n). This improves the O(log^2 n) approximation factor that is trivial to obtain by a direct application of the balanced-separator method.