Drawing Simultaneously Embedded Graphs with Few Bends
نویسندگان
چکیده
منابع مشابه
Drawing Partially Embedded and Simultaneously Planar Graphs
We investigate the problem of constructing planar drawings with few bends for two related problems, the partially embedded graph problem—to extend a straight-line planar drawing of a subgraph to a planar drawing of the whole graph—and the simultaneous planarity problem—to find planar drawings of two graphs that coincide on shared vertices and edges. In both cases we show that if the required pl...
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We consider several variations of the simultaneous embedding problem for planar graphs. We begin with a simple proof that not all pairs of planar graphs have simultaneous geometric embedding. However, using bends, pairs of planar graphs can be simultaneously embedded on the O(n) × O(n) grid, with at most three bends per edge, where n is the number of vertices. The O(n) time algorithm guarantees...
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16 We end this paper by mentioning some open problems and directions for further research: Valiant proved that a grid-area of (n 2) is necessary for drawing non-planar graphs, since the crossing number can be (n 2) 26]. However, the involved constants are very small. For planar graphs (crossing number 0) a drawing with grid-area O(n log 2 n) is possible 14, 26], and the best known lower bound i...
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Given two planar graphs that are defined on the same set of vertices, a RAC simultaneous drawing is a drawing of the two graphs where each graph is drawn planar, no two edges overlap, and edges of one graph can cross edges of the other graph only at right angles. In the geometric version of the problem, vertices are drawn as points and edges as straight-line segments. It is known, however, that...
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