Characterizations and algorithmic applications of chordal graph embeddings

Algorithmic Applications of Low-Distortion Geometric Embeddings

Chordal embeddings of planar graphs

Robertson and Seymour conjectured that the treewidth of a planar graph and the treewidth of its geometric dual differ by at most one. Lapoire solved the conjecture in the affirmative, using algebraic techniques. We give here a much shorter proof of this result.

RDF2Vec: RDF Graph Embeddings and Their Applications

Linked Open Data has been recognized as a valuable source for background information in many data mining and information retrieval tasks. However, most of the existing tools require features in propositional form, i.e., a vector of nominal or numerical features associated with an instance, while Linked Open Data sources are graphs by nature. In this paper, we present RDF2Vec, an approach that u...

Algorithmic embeddings

We present several computationally efficient algorithms, and complexity results on low distortion mappings between metric spaces. An embedding between two metric spaces is a mapping between the two metric spcaes and the distortion of the embedding is the factor by which the distances change. We have pioneered theoretical work on relative (or approximation) version of this problem. In this setti...

An Algorithmic Friedman-Pippenger Theorem on Tree Embeddings and Applications

An (n, d)-expander is a graph G = (V,E) such that for every X ⊆ V with |X| ≤ 2n− 2 we have |ΓG(X)| ≥ (d + 1)|X|. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any (n, d)-expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, ...