R. Tamassia. On-line planar graph embedding. J. Algorithms, 21(2):201--239, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....planarity testing, where the topology is further restricted to upward planar graphs. The updates insert and delete edges as above, and the query is planar(u, v) return yes if and only if the graph remains upward planar after insertion of edge (u, v) This problem was studied by Tamassia [25], who found an O(log n) upper bound. Proposition 3 Upward planarity testing requires time #me n log log n) per operation. A classical problem in Computational Geometry is planar point location: given a subdivision of the plane, i.e. a partition into polygonal regions induced by the straightline ....

R. Tamassia. On-line planar graph embedding. J. Algorithms, 21(2):201--239, 1996.

....fully dynamic reachability algorithms within polylogarithmic time bounds. The only other nontrivial upper bound is the already cited O(n log n) for plane graphs from [63] and recent work of Henzinger and King [31] Other dynamic problems on planar source sink graphs are studied in [6] and [64]. Reference [65] contains pointers to a vast number of applications of these graphs within visibility representations, graph drawing and embedding, motion planning, computational geometry, lattice theory, and VLSI design. 2.1 Reduction to Prefix Parity It is well known how to prove lower bounds ....

Roberto Tamassia. On-line planar graph embedding. Journal of Algorithms, 21(2):201--239, 1996.

....planarity testing, where the topology is further restricted to upward planar graphs. The updates insert and delete edges as above, and the query is planar(u; v) return yes if and only if the graph remains upward planar after insertion of edge (u; v) This problem was studied by Tamassia [24], who found an O(log n) upper bound. Proposition 3. Upward planarity testing requires time Omega Gammame n= log log n) per operation. A classical problem in Computational Geometry is planar point location: given a subdivision of the plane, i.e. a partition into polygonal regions induced by ....

Roberto Tamassia. On-line planar graph embedding. Journal of Algorithms, 21(2):201--239, 1996.

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R. Tamassia. On-line planar graph embedding. J. Algorithms, 21(2):201--239, 1996.

....of the case study. There exist several possible representations for an embedded planar graph, such as the DCEL representation, originally presented in Ref. 64] and later refined (see, e.g. Ref. 21] the quad edge representation [44] and the dynamic representations described in Refs. [29, 30, 81]. Each representation presents advantages and disadvantages, and some may be more suitable than others for a specific application. For instance, in applications in which the embedded planar graph is frequently subject to insertions and deletions of vertices and edges, it is important to be able to ....

R. Tamassia. On-line planar graph embedding. J. Algorithms, 21(2):201--239, 1996.

....the additional information on the ordering of the edges around the vertices, as given by a planar embedding. There exist several topological representations for an embedded planar graph, e.g. the DCEL representation [20] the quad edge representation [9] the dynamic representation described in [22], etc. The interface mechanism allows the implementation of multiple representations for an embedded planar graph. The users of GeomLib can select the most appropriate one by instantiating an object of the corresponding class. They can also implement their own representations, by creating a new ....

R. Tamassia. On-line planar graph embedding. J. Algorithms, 21:201--239, 1996.

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