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» On Paths in a Complete Bipartite Geometric Graph
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DM
2010
128views more  DM 2010»
13 years 6 months ago
Some remarks on the geodetic number of a graph
A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between two not necessarily distinct vertices in D. The geodetic number of G is the minimu...
Mitre Costa Dourado, Fábio Protti, Dieter R...
COMGEO
2007
ACM
13 years 6 months ago
Geometric spanners with applications in wireless networks
In this paper we investigate the relations between spanners, weak spanners, and power spanners in RD for any dimension D and apply our results to topology control in wireless netw...
Christian Schindelhauer, Klaus Volbert, Martin Zie...
CORR
2007
Springer
122views Education» more  CORR 2007»
13 years 6 months ago
How to Complete a Doubling Metric
In recent years, considerable advances have been made in the study of properties of metric spaces in terms of their doubling dimension. This line of research has not only enhanced...
Anupam Gupta, Kunal Talwar
ISAAC
2004
Springer
170views Algorithms» more  ISAAC 2004»
13 years 11 months ago
Spanners, Weak Spanners, and Power Spanners for Wireless Networks
For c ∈ R, a c-spanner is a subgraph of a complete Euclidean graph satisfying that between any two vertices there exists a path of weighted length at most c times their geometric...
Christian Schindelhauer, Klaus Volbert, Martin Zie...
CORR
2010
Springer
134views Education» more  CORR 2010»
13 years 6 months ago
Incremental Sampling-based Algorithms for Optimal Motion Planning
During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs), have been shown to work well in practice and to po...
Sertac Karaman, Emilio Frazzoli