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|Title:||Sparse geometric graphs with small dilation|
De Berg, M.
|Source:||Aronov, B.,De Berg, M.,Cheong, O.,Gudmundsson, J.,Haverkort, H.,Vigneron, A. (2005). Sparse geometric graphs with small dilation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 3827 LNCS : 50-59. ScholarBank@NUS Repository. https://doi.org/10.1007/11602613_7|
|Abstract:||Given a set S of n points in the plane, and an integer k such that 0 ≤ k < n, we show that a geometric graph with vertex set S, at most n - 1 + k edges, and dilation O(n/(k + 1)) can be computed in time O(n log n). We also construct n-point sets for which any geometric graph with n - 1 + k edges has dilation Ω(n/(k + 1)); a slightly weaker statement holds if the points of S are required to be in convex position. © Springer-Verlag Berlin Heidelberg 2005.|
|Source Title:||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Appears in Collections:||Staff Publications|
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