Layerwidth: Analysis of a New Metric for Directed Acyclic Graphs

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.

• Type: Conference
• Year: 2003
• Where: UAI
• Authors: Mark Hopkins
• Keywords: Directed Acyclic Graphs, Important Dag Properties, Structural Model-based Causality, UAI 2003, UAI 2008