Confluent Hasse Diagrams
نویسندگان
چکیده
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(n2) features, in an O(n)×O(n) grid in O(n2) time. For the digraphs representing series-parallel partial orders we show how to construct a drawing with O(n) features in an O(n)×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. Submitted: April 2013 Reviewed: July 2013 Revised: November 2013 Accepted: November 2013 Final: November 2013 Published: November 2013 Article type: Regular paper Communicated by: Antonios Symvonis Research supported in part by NSF grants 0830403 and 1217322 and by the Office of Naval Research under grant N00014-08-1-1015. E-mail addresses: [email protected] (David Eppstein) [email protected] (Joseph A. Simons) 690 Eppstein and Simons Confluent Hasse Diagrams
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