Embedding complex objects as vectors in low dimensional spaces is a longstanding
problem in machine learning. We propose in this work an extension of that approach, which …

We prove that any graph G=(V, E) with n points and m edges has a spanning tree T such
that∑(u, v)∈ E (G) dT (u, v)= O (m log n log log n). Moreover such a tree can be found in …

A central problem in parameterized algorithms is to obtain algorithms with running time
f(k)⋅n^O(1) such that f is as slow growing a function of the parameter k as possible. In …

Based on solid theoretical foundations, we present strong evidence that a number of real‐
world networks, taken from different domains (such as Internet measurements, biological …

An (α, β)-spanner of an unweighted graph G is a subgraph H that distorts distances in G up
to a multiplicative factor of α and an additive term β. It is well known that any graph contains …

A central problem in parameterized algorithms is to obtain algorithms with running time f (k)·
n O (1) such that f is as slow growing function of the parameter k as possible. In particular …

In many real-world applications data appear to be sampled around 1-dimensional
filamentary structures that can be seen as topological metric graphs. In this paper we …

Abstract The Gromov-Hausdorff distance is a natural way to measure the distortion between
two metric spaces. However, there has been only limited algorithmic development to …

Abstract δ-Hyperbolic metric spaces have been defined by M. Gromov in 1987 via a simple 4-
point condition: for any four points u, v, w, x, the two larger of the distance sums d (u, v)+ d …

A spanning tree T of a graph G is called a tree t-spanner of G if the distance between every
pair of vertices in T is at most t times their distance in G. In this paper, we present an …