Parallel Maximum Clique Algorithms with Applications to Network Analysis and Storage

We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks. The method exhibits a roughly linear runtime scaling over real-world networks ranging from 1000 to 100 million nodes. In a test on a social network with 1.8 billion edges, the algorithm finds the largest clique in about 20 minutes. Our method employs a branch and bound strategy with novel and aggressive pruning techniques. For instance, we use the core number of a vertex in combination with a good heuristic clique finder to efficiently remove the vast majority of the search space. In addition, we parallelize the exploration of the search tree. During the search, processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with large search spaces can be pruned by other processes. We apply the algorithm to two problems: to compute temporal strong components and to compress graphs.Comment: 11 page

Scalable Kernelization for Maximum Independent Sets

The most efficient algorithms for finding maximum independent sets in both theory and practice use reduction rules to obtain a much smaller problem instance called a kernel. The kernel can then be solved quickly using exact or heuristic algorithms---or by repeatedly kernelizing recursively in the branch-and-reduce paradigm. It is of critical importance for these algorithms that kernelization is fast and returns a small kernel. Current algorithms are either slow but produce a small kernel, or fast and give a large kernel. We attempt to accomplish both of these goals simultaneously, by giving an efficient parallel kernelization algorithm based on graph partitioning and parallel bipartite maximum matching. We combine our parallelization techniques with two techniques to accelerate kernelization further: dependency checking that prunes reductions that cannot be applied, and reduction tracking that allows us to stop kernelization when reductions become less fruitful. Our algorithm produces kernels that are orders of magnitude smaller than the fastest kernelization methods, while having a similar execution time. Furthermore, our algorithm is able to compute kernels with size comparable to the smallest known kernels, but up to two orders of magnitude faster than previously possible. Finally, we show that our kernelization algorithm can be used to accelerate existing state-of-the-art heuristic algorithms, allowing us to find larger independent sets faster on large real-world networks and synthetic instances.Comment: Extended versio

Navigating Diverse Datasets in the Face of Uncertainty

When exploring big volumes of data, one of the challenging aspects is their diversity of origin. Multiple files that have not yet been ingested into a database system may contain information of interest to a researcher, who must curate, understand and sieve their content before being able to extract knowledge. Performance is one of the greatest difficulties in exploring these datasets. On the one hand, examining non-indexed, unprocessed files can be inefficient. On the other hand, any processing before its understanding introduces latency and potentially un- necessary work if the chosen schema matches poorly the data. We have surveyed the state-of-the-art and, fortunately, there exist multiple proposal of solutions to handle data in-situ performantly. Another major difficulty is matching files from multiple origins since their schema and layout may not be compatible or properly documented. Most surveyed solutions overlook this problem, especially for numeric, uncertain data, as is typical in fields like astronomy. The main objective of our research is to assist data scientists during the exploration of unprocessed, numerical, raw data distributed across multiple files based solely on its intrinsic distribution. In this thesis, we first introduce the concept of Equally-Distributed Dependencies, which provides the foundations to match this kind of dataset. We propose PresQ, a novel algorithm that finds quasi-cliques on hypergraphs based on their expected statistical properties. The probabilistic approach of PresQ can be successfully exploited to mine EDD between diverse datasets when the underlying populations can be assumed to be the same. Finally, we propose a two-sample statistical test based on Self-Organizing Maps (SOM). This method can outperform, in terms of power, other classifier-based two- sample tests, being in some cases comparable to kernel-based methods, with the advantage of being interpretable. Both PresQ and the SOM-based statistical test can provide insights that drive serendipitous discoveries

Generalized gene co-expression analysis via subspace clustering using low-rank representation

BACKGROUND: Gene Co-expression Network Analysis (GCNA) helps identify gene modules with potential biological functions and has become a popular method in bioinformatics and biomedical research. However, most current GCNA algorithms use correlation to build gene co-expression networks and identify modules with highly correlated genes. There is a need to look beyond correlation and identify gene modules using other similarity measures for finding novel biologically meaningful modules. RESULTS: We propose a new generalized gene co-expression analysis algorithm via subspace clustering that can identify biologically meaningful gene co-expression modules with genes that are not all highly correlated. We use low-rank representation to construct gene co-expression networks and local maximal quasi-clique merger to identify gene co-expression modules. We applied our method on three large microarray datasets and a single-cell RNA sequencing dataset. We demonstrate that our method can identify gene modules with different biological functions than current GCNA methods and find gene modules with prognostic values. CONCLUSIONS: The presented method takes advantage of subspace clustering to generate gene co-expression networks rather than using correlation as the similarity measure between genes. Our generalized GCNA method can provide new insights from gene expression datasets and serve as a complement to current GCNA algorithms