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arXiv · 1212.2479

LAYERWIDTH: Analysis of a New Metric for Directed Acyclic Graphs

Mark Hopkins
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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.

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Mark Hopkins. 2012-10-19. LAYERWIDTH: Analysis of a New Metric for Directed Acyclic Graphs. https://arxiv.org/abs/1212.2479

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