Designing Optimal Flow Networks

TL;DR

This paper studies the optimal design of flow networks with minimal cost, focusing on tree structures called MGAs for concave increasing costs, and characterizes Steiner points for linear costs, relevant to infrastructure design.

Contribution

It characterizes the local structure of Steiner points in MGAs with linear cost functions, advancing understanding of optimal flow network design.

Findings

MGAs have a tree topology for concave increasing costs

Characterization of Steiner points in MGAs for linear costs

Applications to drain, pipeline, and mine access network design

Abstract

We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations and flows. The network may contain other unprescribed nodes, known as Steiner points. For concave increasing cost functions, a minimum cost network of this sort has a tree topology, and hence can be called a Minimum Gilbert Arborescence (MGA). We characterise the local topological structure of Steiner points in MGAs for linear cost functions. This problem has applications to the design of drains, gas pipelines and underground mine access.