LAYERWIDTH: Analysis of a New Metric for Directed Acyclic Graphs

TL;DR

This paper introduces and analyzes the layerwidth property of directed acyclic graphs (DAGs), establishing its computational complexity, properties, and relation to other DAG metrics, with implications for structural causality problems.

Contribution

It proves NP-completeness of deciding bounded layerwidth and explores properties that facilitate efficient computation of optimal layerwidth.

Findings

Deciding bounded layerwidth is NP-complete.

Layerwidth has important properties for computation.

Compared layerwidth with treewidth and bandwidth.

Abstract

We analyze a new property of directed acyclic graphs (DAGs), called layerwidth, arising from a class of DAGs proposed by Eiter and Lukasiewicz. This class of DAGs permits certain problems of structural model-based causality and explanation to be tractably solved. In this paper, we first address an open question raised by Eiter and Lukasiewicz - the computational complexity of deciding whether a given graph has a bounded layerwidth. After proving that this problem is NP-complete, we proceed by proving numerous important properties of layerwidth that are helpful in efficiently computing the optimal layerwidth. Finally, we compare this new DAG property to two other important DAG properties: treewidth and bandwidth.