# Shared-Memory Branch-and-Reduce for Multiterminal Cuts

## TL;DR

This paper presents a highly efficient exact algorithm for the multiterminal cut problem, leveraging data reduction rules within a branch-and-reduce framework to significantly outperform traditional ILP methods in solving larger instances.

## Contribution

The paper introduces new data reduction rules and integrates them into a branch-and-reduce framework, achieving unprecedented speedups for solving multiterminal cut problems.

## Key findings

- Achieves up to multiple orders of magnitude faster runtimes than standard ILP methods.
- Enables solving larger instances to optimality than previously possible.
- Demonstrates the effectiveness of data reduction rules in exact algorithms.

## Abstract

We introduce the fastest known exact algorithm~for~the multiterminal cut problem with k terminals. In particular, we engineer existing as well as new data reduction rules. We use the rules within a branch-and-reduce framework and to boost the performance of an ILP formulation. Our algorithms achieve improvements in running time of up to multiple orders of magnitudes over the ILP formulation without data reductions, which has been the de facto standard used by practitioners. This allows us to solve instances to optimality that are significantly larger than was previously possible.