Algorithm Engineering for Cut Problems

TL;DR

This paper develops highly-efficient algorithms for various graph cut problems, including minimum cut, balanced partitioning, and multiterminal cut, applicable to large-scale networks across different domains.

Contribution

It introduces practical, efficient algorithms for multiple graph cut problems, with implementations freely available, advancing the state-of-the-art in algorithm engineering.

Findings

Algorithms are highly efficient in practice.

Algorithms are applicable to large-scale networks.

Implementations are freely available for use.

Abstract

Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut networks into smaller, more readily comprehensible blocks. In this work, we aim to partition the vertices of a graph into multiple blocks while minimizing the number of edges that connect different blocks. There is a multitude of cut or partitioning problems that have been the focus of research for multiple decades. This work develops highly-efficient algorithms for the (global) minimum cut problem, the balanced graph partitioning problem and the multiterminal cut problem. All of these algorithms are efficient in practice and freely available for use.