Simultaneous Embedding of Planar Graphs with Few Bends
Erten, Cesim and Kobourov, Stephen G. (2004) Simultaneous Embedding of Planar Graphs with Few Bends. In: Graph Drawing 12th International Symposium, GD 2004, September 29-October 2, 2004, New York, NY, USA , pp. 195-205 (Official URL: http://dx.doi.org/10.1007/978-3-540-31843-9_21).
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We present an O(n) time algorithm for simultaneous embedding of pairs of planar graphs on the O(n^2)× O(n^2) grid, with at most three bends per edge, where n is the number of vertices. For the case when the input graphs are both trees, only one bend per edge is required. We also describe an O(n) time algorithm for simultaneous embedding with fixed-edges for tree-path pairs on the O(n)× O(n^2) grid with at most one bend per tree-edge and no bends along path edges. This work is partially supported by the NSF under grant ACR-0222920 and by ITCDI under grant 003297.
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