GraphMineSuite: Enabling High-Performance and Programmable Graph Mining Algorithms with Set Algebra

We propose GraphMineSuite (GMS): the first benchmarking suite for graph mining that facilitates evaluating and constructing high-performance graph mining algorithms. First, GMS comes with a benchmark specification based on extensive literature review, prescribing representative problems, algorithms, and datasets. Second, GMS offers a carefully designed software platform for seamless testing of different fine-grained elements of graph mining algorithms, such as graph representations or algorithm subroutines. The platform includes parallel implementations of more than 40 considered baselines, and it facilitates developing complex and fast mining algorithms. High modularity is possible by harnessing set algebra operations such as set intersection and difference, which enables breaking complex graph mining algorithms into simple building blocks that can be separately experimented with. GMS is supported with a broad concurrency analysis for portability in performance insights, and a novel performance metric to assess the throughput of graph mining algorithms, enabling more insightful evaluation. As use cases, we harness GMS to rapidly redesign and accelerate state-of-the-art baselines of core graph mining problems: degeneracy reordering (by up to >2x), maximal clique listing (by up to >9x), k-clique listing (by 1.1x), and subgraph isomorphism (by up to 2.5x), also obtaining better theoretical performance bounds

High-Performance Parallel Graph Coloring with Strong Guarantees on Work, Depth, and Quality

We develop the first parallel graph coloring heuristics with strong theoretical guarantees on work and depth and coloring quality. The key idea is to design a relaxation of the vertex degeneracy order, a well-known graph theory concept, and to color vertices in the order dictated by this relaxation. This introduces a tunable amount of parallelism into the degeneracy ordering that is otherwise hard to parallelize. This simple idea enables significant benefits in several key aspects of graph coloring. For example, one of our algorithms ensures polylogarithmic depth and a bound on the number of used colors that is superior to all other parallelizable schemes, while maintaining workefficiency. In addition to provable guarantees, the developed algorithms have competitive run-times for several real-world graphs, while almost always providing superior coloring quality. Our degeneracy ordering relaxation is of separate interest for algorithms outside the context of coloring

ProbGraph: High-Performance and High-Accuracy Graph Mining with Probabilistic Set Representations

Important graph mining problems such as Clustering are computationally demanding. To significantly accelerate these problems, we propose ProbGraph: a graph representation that enables simple and fast approximate parallel graph mining with strong theoretical guarantees on work, depth, and result accuracy. The key idea is to represent sets of vertices using probabilistic set representations such as Bloom filters. These representations are much faster to process than the original vertex sets thanks to vectorizability and small size. We use these representations as building blocks in important parallel graph mining algorithms such as Clique Counting or Clustering. When enhanced with ProbGraph, these algorithms significantly outperform tuned parallel exact baselines (up to nearly 50x on 32 cores) while ensuring accuracy of more than 90% for many input graph datasets. Our novel bounds and algorithms based on probabilistic set representations with desirable statistical properties are of separate interest for the data analytics community

Metabolic syndrome is associated with similar long-term prognosis in non-obese and obese patients. An analysis of 45 615 patients from the nationwide LIPIDOGRAM 2004-2015 cohort studies

Aims We aimed to evaluate the association between metabolic syndrome (MetS) and long-term all-cause mortality. Methods The LIPIDOGRAM studies were carried out in the primary care in Poland in 2004, 2006 and 2015. MetS was diagnosed based on the National Cholesterol Education Program, Adult Treatment Panel III (NCEP/ATP III) and Joint Interim Statement (JIS) criteria. The cohort was divided into four groups: non-obese patients without MetS, obese patients without MetS, non-obese patients with MetS and obese patients with MetS. Differences in all-cause mortality was analyzed using Kaplan-Meier and Cox regression analyses. Results 45,615 participants were enrolled (mean age 56.3, standard deviation: 11.8 years; 61.7% female). MetS was diagnosed in 14,202 (31%) by NCEP/ATP III criteria, and 17,216 (37.7%) by JIS criteria. Follow-up was available for 44,620 (97.8%, median duration 15.3 years) patients. MetS was associated with increased mortality risk among the obese (hazard ratio, HR: 1.88 [95% CI, 1.79-1.99] and HR: 1.93 [95% CI 1.82-2.04], according to NCEP/ATP III and JIS criteria, respectively) and non-obese individuals (HR: 2.11 [95% CI 1.85-2.40] and 1.7 [95% CI, 1.56-1.85] according to NCEP/ATP III and JIS criteria respectively). Obese patients without MetS had a higher mortality risk than non-obese patients without MetS (HR: 1.16 [95% CI 1.10-1.23] and HR: 1.22 [95%CI 1.15-1.30], respectively in subgroups with NCEP/ATP III and JIS criteria applied). Conclusions MetS is associated with increased all-cause mortality risk in non-obese and obese patients. In patients without MetS obesity remains significantly associated with mortality. The concept of metabolically healthy obesity should be revised