Embedding metrics into constant-dimensional geometric spaces, such as the Euclidean plane, is relatively poorly understood. Motivated by applications in visualization, ad-hoc netw...
MohammadHossein Bateni, Mohammad Taghi Hajiaghayi,...
Spectral methods for nonlinear dimensionality reduction (NLDR) impose a neighborhood graph on point data and compute eigenfunctions of a quadratic form generated from the graph. W...
In this paper we study the cycle base structures of embedded graphs on surfaces. We first give a sufficient and necessary condition for a set of facial cycles to be contained in ...
We present fast algorithms for constructing probabilistic embeddings and approximate distance oracles in sparse graphs. The main ingredient is a fast algorithm for sampling the pr...
This paper shows that any planar graph with n vertices can be point-set embedded with at most one bend per edge on a universal set of n points in the plane. An implication of this...
Hazel Everett, Sylvain Lazard, Giuseppe Liotta, St...