A poset metric from the directed maximum common edge subgraph
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We study the directed maximum common edge subgraph problem (DMCES) for directed graphs. We use DMCES to define a metric on partially ordered sets. While most existing metrics assume that the underlying sets of the partial order are identical, and only the relationships between elements can differ, the metric defined here allows the partially ordered sets to be of different sizes. The proof that there is a metric based on DMCES involves the extension of the concept of line digraphs. Although this extension can be used directly to compute the metric, it is computationally feasible only for sparse graphs. We provide algorithms for computing the metric for dense graphs and transitively closed graphs.
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