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- Urquhart_graph abstract "In computational geometry, the Urquhart graph of a set of points in the plane, named after Roderick B. Urquhart, is obtained by removing the longest edge from each triangle in the Delaunay triangulation.The Urquhart graph was described by Urquhart (1980), who suggested that removing the longest edge from each Delaunay triangle would be a fast way of constructing the relative neighborhood graph (the graph connecting pairs of points p and q when there does not exist any third point r that is closer to both p and q than they are to each other). Since Delaunay triangulations can be constructed in time O(n log n), the same time bound holds for the Urquhart graph as well. Although it was later shown that the Urquhart graph is not exactly the same as the relative neighborhood graph, it can be used as a good approximation to it. The problem of constructing relative neighborhood graphs in O(n log n) time, left open by the mismatch between the Urquhart graph and the relative neighborhood graph, was solved by Supowit (1983).Like the relative neighborhood graph, the Urquhart graph of a set of points in general position contains the Euclidean minimum spanning tree of its points, from which it follows that it is a connected graph.".
- Urquhart_graph thumbnail Urquhart_graph.svg?width=300.
- Urquhart_graph wikiPageID "24438021".
- Urquhart_graph wikiPageLength "2806".
- Urquhart_graph wikiPageOutDegree "11".
- Urquhart_graph wikiPageRevisionID "667273934".
- Urquhart_graph wikiPageWikiLink Category:Computational_geometry.
- Urquhart_graph wikiPageWikiLink Category:Geometric_graphs.
- Urquhart_graph wikiPageWikiLink Computational_geometry.
- Urquhart_graph wikiPageWikiLink Connectivity_(graph_theory).
- Urquhart_graph wikiPageWikiLink Delaunay_triangulation.
- Urquhart_graph wikiPageWikiLink Edge_(geometry).
- Urquhart_graph wikiPageWikiLink Euclidean_minimum_spanning_tree.
- Urquhart_graph wikiPageWikiLink General_position.
- Urquhart_graph wikiPageWikiLink Relative_neighborhood_graph.
- Urquhart_graph wikiPageWikiLink Triangle.
- Urquhart_graph wikiPageWikiLink File:Urquhart_graph.svg.
- Urquhart_graph wikiPageWikiLinkText "Urquhart graph".
- Urquhart_graph wikiPageUsesTemplate Template:Harvtxt.
- Urquhart_graph wikiPageUsesTemplate Template:Reflist.
- Urquhart_graph subject Category:Computational_geometry.
- Urquhart_graph subject Category:Geometric_graphs.
- Urquhart_graph type Algorithm.
- Urquhart_graph comment "In computational geometry, the Urquhart graph of a set of points in the plane, named after Roderick B.".
- Urquhart_graph label "Urquhart graph".
- Urquhart_graph sameAs Q2811423.
- Urquhart_graph sameAs Urquhartgraaf.
- Urquhart_graph sameAs m.080d7__.
- Urquhart_graph sameAs Q2811423.
- Urquhart_graph wasDerivedFrom Urquhart_graph?oldid=667273934.
- Urquhart_graph depiction Urquhart_graph.svg.
- Urquhart_graph isPrimaryTopicOf Urquhart_graph.