LAYERWIDTH: Analysis of a New Metric for Directed Acyclic Graphs
This addresses an open problem in structural model-based causality and explanation, providing foundational insights for researchers in graph theory and AI, though it is incremental on prior work.
The paper tackles the computational complexity of determining if a directed acyclic graph (DAG) has bounded layerwidth, proving it is NP-complete, and analyzes properties to compute optimal layerwidth efficiently, comparing it to treewidth and bandwidth.
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.