# Faster and Better Nested Dissection Orders for Customizable Contraction Hierarchies

## TL;DR

This paper introduces a new method combining flow-based graph bipartitioning algorithms to significantly accelerate nested dissection order computation for Customizable Contraction Hierarchies, improving preprocessing and query times in road networks.

## Contribution

It presents a novel combination of FlowCutter and Inertial Flow algorithms to enhance the speed and quality of nested dissection orders for CCH, outperforming previous methods.

## Key findings

- Over six times faster preprocessing than FlowCutter
- Faster query times on the Europe road network
- Preprocessing completed in four minutes using 16 cores

## Abstract

Graph partitioning has many applications. We consider the acceleration of shortest path queries in road networks using Customizable Contraction Hierarchies (CCH). It is based on computing a nested dissection order by recursively dividing the road network into parts. Recently, with FlowCutter and Inertial Flow, two flow-based graph bipartitioning algorithms have been proposed for road networks. While FlowCutter achieves high-quality results and thus fast query times, it is rather slow. Inertial Flow is particularly fast due to the use of geographical information while still achieving decent query times. We combine the techniques of both algorithms to achieve more than six times faster preprocessing times than FlowCutter and even faster queries on the Europe road network. We show that using 16 cores of a shared-memory machine, this preprocessing needs four minutes.