An n-vertex graph is equitably k-colorable if there is a proper coloring of its vertices such that each color is used either n/k or n/k times. While classic Vertex Coloring is fixed parameter tractable under well established parameters such as pathwidth and feedback vertex set, equitable coloring is W[1]-hard. We prove that Equitable Coloring is fixed parameter tractable when parameterized by distance to cluster or co-cluster graphs, improving on the FPT algorithm of Fiala et al. ( 2011) parameterized by vertex cover. In terms of intractability, we adapt the proof of Fellows et al. (2011) to show that Equitable Coloring is W[1]-hard when simultaneously parameterized by distance to disjoint paths and number of colors. We also revisit the literature and derive other results on the parameterized complexity of the problem through minor reductions or other simple observations.

We here propose a new method for expanding entity related queries that automatically filters, weights and ranks candidate expasion terms extracted from Wikipedia articles related to the original query. Our method is based on stateof-the-art tag recommendation methods that exploit heuristic metrics to estimate the descriptive capacity of a given term. Originally proposed for the context of tags, we here apply these recommendation methods to weight and rank terms extracted from multiple fields of Wikipedia articles according to their relevance for the article. We evaluate our method comparing it against three state-of-the-art baselines in three collections. Our results indicate that our method outperforms all baselines in all collections, with relative gains in MAP of up to 14% against the best ones.

No abstract

No abstract

In this work, we consider hypothesis testing and anomaly detection on datasets where each observation is a weighted network. Examples of such data include brain connectivity networks from fMRI flow data, or word co-occurrence counts for populations of individuals. Current approaches to hypothesis testing for weighted networks typically requires thresholding the edge-weights, to transform the data to binary networks. This results in a loss of information, and outcomes are sensitivity to choice of threshold levels. Our work avoids this, and we consider weighted-graph observations in two situations, 1) where each graph belongs to one of two populations, and 2) where entities belong to one of two populations, with each entity possessing multiple graphs (indexed e.g. by time). Specifically, we propose a hierarchical Bayesian hypothesis testing framework that models each population with a mixture of latent space models for weighted networks, and then tests populations of networks for differences in distribution over components. Our framework is capable of population-level, entity-specific, as well as edge-specific hypothesis testing. We apply it to synthetic data and three real-world datasets: two social media datasets involving word co-occurrences from discussions on Twitter of the political unrest in Brazil, and on Instagram concerning Attention Deficit Hyperactivity Disorder (ADHD) and depression drugs, and one medical dataset involving fMRI brain-scans of human subjects. The results show that our proposed method has lower Type I error and higher statistical power compared to alternatives that need to threshold the edge weights. Moreover, they show our proposed method is better suited to deal with highly heterogeneous datasets.