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\title{Transitive closure according to Roy-Floyd-Warshall}
\author{Makarius Wenzel}
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\begin{abstract}
This formulation of the Roy-Floyd-Warshall algorithm for the transitive
closure bypasses matrices and arrays, but uses a more direct mathematical
model with adjacency functions for immediate predecessors and successors.
This can be implemented efficiently in functional programming languages and
is particularly adequate for sparse relations.
\end{abstract}

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