Crossings and Planarization
نویسندگان
چکیده
Petra Mutzel TU Dortmund 2.
منابع مشابه
Linear-time algorithms for geometric graphs with sublinearly many crossings
We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an iterated logarithmic factor. Specific problems we study include Voronoi diagrams and single-source shortest paths. Our algorithms all run in linear time in the ...
متن کاملLinear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings
We provide linear-time algorithms for geometric graphs with sublinearly many edge crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an iterated logarithmic factor. Specific problems we study include Voronoi diagrams and single-source shortest paths. Our algorithms all run in linear time in...
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Drawing directed graphs has many applications and occurs whenever a natural flow of information is to be visualized. Given a directed acyclic graph (DAG) G, we are interested in an upward drawing of G, that is, a drawing of G in which all arcs are drawn as curves that are monotonically increasing in the vertical direction. Besides the upward property, it is desirable that the number of arc cros...
متن کاملOptimal k-Level Planarization and Crossing Minimization
An important step in laying out hierarchical network diagrams is to order the nodes on each level. The usual approach is to minimize the number of edge crossings. This problem is NP-hard even for two layers when the first layer is fixed. Hence, in practice crossing minimization is performed using heuristics. Another suggested approach is to maximize the planar subgraph, i.e. find the least numb...
متن کاملNotes in Computer Science 2265
A bipartite graph is biplanar if the vertices can be placed on two parallel lines (layers) in the plane such that there are no edge crossings when edges are drawn straight. The 2-Layer Planarization problem asks if k edges can be deleted from a given graph G so that the remaining graph is biplanar. This problem is NP-complete, as is the 1Layer Planarization problem in which the permutation of t...
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تاریخ انتشار 2013