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GD
2006
Springer
14 years 4 days ago
Computing Geometric Minimum-Dilation Graphs Is NP-Hard
We prove that computing a geometric minimum-dilation graph on a given set of points in the plane, using not more than a given number of edges, is an NP-hard problem, no matter if ...
Rolf Klein, Martin Kutz
COMBINATORICA
2008
88views more  COMBINATORICA 2008»
13 years 8 months ago
Geometric graphs with no two parallel edges
We give a simple proof for a theorem of Katchalski, Last, and Valtr, asserting that the maximum number of edges in a geometric graph G on n vertices with no pair of parallel edges...
Rom Pinchasi
BIOINFORMATICS
2008
172views more  BIOINFORMATICS 2008»
13 years 8 months ago
Fitting a geometric graph to a protein-protein interaction network
Motivation: Finding a good network null model for protein-protein interaction (PPI) networks is a fundamental issue. Such a model would provide insights into the interplay between...
Desmond J. Higham, Marija Rasajski, Natasa Przulj
ICDCS
2008
IEEE
14 years 2 months ago
Distributed Connected Dominating Set Construction in Geometric k-Disk Graphs
In this paper, we study the problem of minimum connected dominating set in geometric k-disk graphs. This research is motivated by the problem of virtual backbone construction in w...
Kai Xing, Wei Cheng, E. K. Park, Shmuel Rotenstrei...
ISAAC
2005
Springer
91views Algorithms» more  ISAAC 2005»
14 years 2 months ago
Sparse Geometric Graphs with Small Dilation
Given a set S of n points in RD , 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, maximum degree five, and dila...
Boris Aronov, Mark de Berg, Otfried Cheong, Joachi...