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COMPGEOM
1993
ACM

Worst-Case Bounds for Subadditive Geometric Graphs

9 years 4 months ago
Worst-Case Bounds for Subadditive Geometric Graphs
We consider graphs such as the minimum spanning tree, minimum Steiner tree, minimum matching, and traveling salesman tour for n points in the d-dimensional unit cube. For each of these graphs, we show that the worst-case sum of the dth powers of edge lengths is O(log n). This is a consequence of a general “gap theorem”: for any subadditive geometric graph, either the worst-case sum of edge lengths is O(n(d−1)/d ) and the sum of dth powers is O(log n), or the sum of edge lengths is Ω(n). We look more closely at some specific graphs: the worst-case sum of dth powers is O(1) for minimum matching, but Ω(log n) for traveling salesman tour, which answers a question of Snyder and Steele.
Marshall W. Bern, David Eppstein
Added 09 Aug 2010
Updated 09 Aug 2010
Type Conference
Year 1993
Where COMPGEOM
Authors Marshall W. Bern, David Eppstein
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