Michele Borassi

Into the Square

We analyze several quadratic-time solvable problems, and we show that these problems are not solvable in truly subquadratic time (that is, in time O(n2-?) for some ?>0), unless the well known Strong Exponential Time Hypothesis (in short, SETH) is false. In particular, we start from an artificial quadratic-time solvable variation of the k-Sat problem (already introduced and used in the literature) and we will construct a web of Karp reductions, proving that a truly subquadratic-time algorithm for any of the problems in the web falsifies SETH. Some of these results were already known, while others are, as far as we know, new. The new problems considered are: computing the betweenness centrality of a vertex (the same result was proved independently by Abboud et al.), computing the minimum closeness centrality in a graph, computing the hyperbolicity of a graph, and computing the subset graph of a collection of sets. On the other hand, we will show that testing if a directed graph is transitive and testing if a graph is a comparability graph are subquadratic-time solvable (our algorithm is practical, since it is not based on intricate matrix multiplication algorithms).

On Computing the Hyperbolicity of Real-World Graphs

The (Gromov) hyperbolicity is a topological property of a graph, which has been recently applied in several different contexts, such as the design of routing schemes, network security, computational biology, the analysis of graph algorithms, and the classification of complex networks. Computing the hyperbolicity of a graph can be very time consuming: indeed, the best available algorithm has running-time \(\mathcal{O}(n^{3.69})\), which is clearly prohibitive for big graphs. In this paper, we provide a new and more efficient algorithm: although its worst-case complexity is \(\mathcal{O}(n^4)\), in practice it is much faster, allowing, for the first time, the computation of the hyperbolicity of graphs with up to 200,000 nodes. We experimentally show that our new algorithm drastically outperforms the best previously available algorithms, by analyzing a big dataset of real-world networks. Finally, we apply the new algorithm to compute the hyperbolicity of random graphs generated with the Erdos-Renyi model, the Chung-Lu model, and the Configuration Model.

Telling metabolic stories to explore metabolomics data: A case study on the Yeast response to cadmium exposure

Motivation: The increasing availability of metabolomics data enables to better understand the metabolic processes involved in the immediate response of an organism to environmental changes and stress. The data usually come in the form of a list of metabolites whose concentrations significantly changed under some conditions, and are thus not easy to interpret without being able to precisely visualize how such metabolites are interconnected. Results: We present a method that enables to organize the data from any metabolomics experiment into metabolic stories. Each story corresponds to a possible scenario explaining the flow of matter between the metabolites of interest. These scenarios may then be ranked in different ways depending on which interpretation one wishes to emphasize for the causal link between two affected metabolites: enzyme activation, enzyme inhibition or domino effect on the concentration changes of substrates and products. Equally probable stories under any selected ranking scheme can be further grouped into a single anthology that summarizes, in a unique subnetwork, all equivalently plausible alternative stories. An anthology is simply a union of such stories. We detail an application of the method to the response of yeast to cadmium exposure. We use this system as a proof of concept for our method, and we show that we are able to find a story that reproduces very well the current knowledge about the yeast response to cadmium. We further show that this response is mostly based on enzyme activation. We also provide a framework for exploring the alternative pathways or side effects this local response is expected to have in the rest of the network. We discuss several interpretations for the changes we see, and we suggest hypotheses that could in principle be experimentally tested. Noticeably, our method requires simple input data and could be used in a wide variety of applications. Availability and implementation: The code for the method presented in this article is available at http://gobbolino.gforge.inria.fr. Contact: pvmilreu@gmail.com; vincent.lacroix@univ-lyon1.fr; marie-france.sagot@inria.fr Supplementary information: Supplementary data are available at Bioinformatics online.

KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation

We present KADABRA, a new algorithm to approximate betweenness centrality in directed and undirected graphs, which significantly outperforms all previous approaches on real-world complex networks. The efficiency of the new algorithm relies on two new theoretical contributions, of independent interest. The first contribution focuses on sampling shortest paths, a subroutine used by most algorithms that approximate betweenness centrality. We show that, on realistic random graph models, we can perform this task in time

On the Solvability of the Six Degrees of Kevin Bacon Game

|E|^{\frac{1}{2}+o(1)}

An axiomatic and an average-case analysis of algorithms and heuristics for metric properties of graphs

with high probability, obtaining a significant speedup with respect to the

Telling Stories Fast

\Theta(|E|)

Fast diameter and radius BFS-based computation in (weakly connected) real-world graphs

worst-case performance. We experimentally show that this new technique achieves similar speedups on real-world complex networks, as well. The second contribution is a new rigorous application of the adaptive sampling technique. This approach decreases the total number of shortest paths that need to be sampled to compute all betweenness centralities with a given absolute error, and it also handles more general problems, such as computing the

Computing Top-k Closeness Centrality Faster in Unweighted Graphs

k

On the Solvability of the Six Degrees of Kevin Bacon Game - A Faster Graph Diameter and Radius Computation Method.

most central nodes. Furthermore, our analysis is general, and it might be extended to other settings.