# Understanding the Effectiveness of Data Reduction in Public Transportation Networks

## TL;DR

This paper investigates why simple reduction rules efficiently solve minimum hitting set problems in real-world transportation networks, highlighting locality as a key factor and demonstrating its prevalence across various domains.

## Contribution

The study introduces a randomized model for hitting set instances, identifies locality as crucial for reduction effectiveness, and proves its independence from graph structure.

## Key findings

- Locality significantly impacts reduction success.
- Heterogeneity influences reduction but is less critical.
- High locality is common in diverse problem domains.

## Abstract

Given a public transportation network of stations and connections, we want to find a minimum subset of stations such that each connection runs through a selected station. Although this problem is NP-hard in general, real-world instances are regularly solved almost completely by a set of simple reduction rules. To explain this behavior, we view transportation networks as hitting set instances and identify two characteristic properties, locality and heterogeneity. We then devise a randomized model to generate hitting set instances with adjustable properties. While the heterogeneity does influence the effectiveness of the reduction rules, the generated instances show that locality is the significant factor. Beyond that, we prove that the effectiveness of the reduction rules is independent of the underlying graph structure. Finally, we show that high locality is also prevalent in instances from other domains, facilitating a fast computation of minimum hitting sets.