We consider the problem of preprocessing an n-vertex digraph with real edge weights so that subsequent queries for the shortest path or distance between any two vertices can be efï...
The weight of a randomly chosen link in the shortest path tree on the complete graph with exponential i.i.d. link weights is studied. The corresponding exact probability generatin...
Numerous cognitive studies have indicated that the form and complexity of route instructions may be as important to human navigators as the overall length of route. Most automated ...
This a summary of the author's PhD thesis supervised by Leo Liberti, Philippe Baptiste and Daniel Krob and defended on 18 June 2009 at Ecole Polytechnique, Palaiseau, France. ...
There are several results available in the literature dealing with efficient construction of t-spanners for a given set S of n points in Rd. t-spanners are Euclidean graphs in whic...