6 research outputs found
Traveling in randomly embedded random graphs
We consider the problem of traveling among random points in Euclidean space,
when only a random fraction of the pairs are joined by traversable connections.
In particular, we show a threshold for a pair of points to be connected by a
geodesic of length arbitrarily close to their Euclidean distance, and analyze
the minimum length Traveling Salesperson Tour, extending the
Beardwood-Halton-Hammersley theorem to this setting.Comment: 25 pages, 2 figure
Traveling in Randomly Embedded Random Graphs
We consider the problem of traveling among random points in Euclidean space, when only a random fraction of the pairs are joined by traversable connections. In particular, we show a threshold for a pair of points to be connected by a geodesic of length arbitrarily close to their Euclidean distance, and analyze the minimum length Traveling Salesperson Tour, extending the Beardwood-Halton-Hammersley theorem to this setting
A note on dispersing particles on a line
We consider a synchronous dispersion process introduced in \cite{CRRS} and we
show that on the infinite line the final set of occupied sites takes up
space, where is the number of particles involved