LAYERWIDTH: Analysis of a New Metric for Directed Acyclic Graphs
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.
Cite
@article{arxiv.1212.2479,
title = {LAYERWIDTH: Analysis of a New Metric for Directed Acyclic Graphs},
author = {Mark Hopkins},
journal= {arXiv preprint arXiv:1212.2479},
year = {2012}
}
Comments
Appears in Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence (UAI2003)