The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix-based graph algorithms to the broadest possible audience. Mathematically, the GraphBLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, the two are easily connected by matrix multiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of a small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.
Abstract-The Apache Accumulo database excels at distributed storage and indexing and is ideally suited for storing graph data. Many big data analytics compute on graph data and persist their results back to the database. These graph calculations are often best performed inside the database server. The GraphBLAS standard provides a compact and efficient basis for a wide range of graph applications through a small number of sparse matrix operations. In this article, we discuss a serverside implementation of GraphBLAS sparse matrix multiplication that leverages Accumulo's native, high-performance iterators. We compare the mathematics and performance of inner and outer product implementations, and show how an outer product implementation achieves optimal performance near Accumulo's peak write rate. We offer our work as a core component to the Graphulo library that will deliver matrix math primitives for graph analytics within Accumulo.
Abstract-Big data and the Internet of Things era continue to challenge computational systems. Several technology solutions such as NoSQL databases have been developed to deal with this challenge. In order to generate meaningful results from large datasets, analysts often use a graph representation which provides an intuitive way to work with the data. Graph vertices can represent users and events, and edges can represent the relationship between vertices. Graph algorithms are used to extract meaningful information from these very large graphs. At MIT, the Graphulo initiative is an effort to perform graph algorithms directly in NoSQL databases such as Apache Accumulo or SciDB, which have an inherently sparse data storage scheme. Sparse matrix operations have a history of efficient implementations and the Graph Basic Linear Algebra Subprogram (GraphBLAS) community has developed a set of key kernels that can be used to develop efficient linear algebra operations. However, in order to use the GraphBLAS kernels, it is important that common graph algorithms be recast using the linear algebra building blocks. In this article, we look at common classes of graph algorithms and recast them into linear algebra operations using the GraphBLAS building blocks.
Abstract-The success of SQL, NoSQL, and NewSQL databases is a reflection of their ability to provide significant functionality and performance benefits for specific domains, such as financial transactions, internet search, and data analysis. The BigDAWG polystore seeks to provide a mechanism to allow applications to transparently achieve the benefits of diverse databases while insulating applications from the details of these databases. Associative arrays provide a common approach to the mathematics found in different databases: sets (SQL), graphs (NoSQL), and matrices (NewSQL). This work presents the SQL relational model in terms of associative arrays and identifies the key mathematical properties that are preserved within SQL. These properties include associativity, commutativity, distributivity, identities, annihilators, and inverses. Performance measurements on distributivity and associativity show the impact these properties can have on associative array operations. These results demonstrate that associative arrays could provide a mathematical model for polystores to optimize the exchange of data and execution queries.
Specimens, parts and products of threatened species are commonly traded on the internet. This could threaten the survival of some wild populations. We outline 2 methods to monitor internet sales of species to assess potential threats and inform conservation actions. Our first method combines systematic monitoring of online offers of plants for sale with expert consultation. Our second method utilises a computational model, trained to expert-classified records using probabilistic inference, to predict unknown properties of the traded taxa. We used these methods to monitor internet trade in 5 genera of succulent plant species endemic to Madagascar, some of which have recently been listed for trade regulation under the Convention on International Trade in Endangered Species (CITES). This revealed potential threats to wild populations: for instance, almost all species recorded were of high conservation concern, yet most offers for live plants were of apparently wild-collected specimens (85%). Our model predicted with 89% accuracy whether the plants were classified as propagated or wild collected by an expert, although accuracy dropped for data collected in the following summer. Our results highlight potential threats by internet trade to the survival of some CITES and non-CITES listed plant species from Madagascar. These should be addressed by further conservation actions and policy. More generally, our results reveal how standardised internet surveys can provide information on levels of trade in wild-collected threatened species that could impact on natural populations, and can provide data that can be incorporated into models to facilitate future monitoring and enforcement.
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