Confluent Hasse diagrams

Computer Science – Computational Geometry

Scientific paper

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12 pages, 8 figures

Scientific paper

We show that a transitively reduced digraph has a confluent upward drawing if and only if its reachability relation has order dimension at most two. In this case, we construct a confluent upward drawing with $O(n^2)$ features, in an $O(n) \times O(n)$ grid in O(n^2) time. For the digraphs representing series-parallel partial orders we show how to construct a drawing with O(n) features in an $O(n) \times O(n)$ grid in O(n) time from a series-parallel decomposition of the partial order. Our drawings are optimal in the number of confluent junctions they use.

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