The Minimum Edit Arborescence Problem and Its Use in Compressing Graph Collections [Extended Version]

TL;DR

This paper introduces the edit arborescence framework, a unified approach for modeling and solving minimum spanning arborescences based on edit paths, which can be applied to efficiently compress collections of labeled graphs.

Contribution

It presents the Min Edit Arborescence Problem and demonstrates its application in graph collection compression using encoding size-preserving edit costs.

Findings

Effective graph compression compared to standard tools

Versatile framework applicable to various data types

Potential for broad application in unsupervised learning

Abstract

The inference of minimum spanning arborescences within a set of objects is a general problem which translates into numerous application-specific unsupervised learning tasks. We introduce a unified and generic structure called edit arborescence that relies on edit paths between data in a collection, as well as the Min Edit Arborescence Problem, which asks for an edit arborescence that minimizes the sum of costs of its inner edit paths. Through the use of suitable cost functions, this generic framework allows to model a variety of problems. In particular, we show that by introducing encoding size preserving edit costs, it can be used as an efficient method for compressing collections of labeled graphs. Experiments on various graph datasets, with comparisons to standard compression tools, show the potential of our method.