Steven P. Reinhardt

High-performance graph algorithms from parallel sparse matrices

Large-scale computation on graphs and other discrete structures is becoming increasingly important in many applications, including computational biology, web search, and knowledge discovery. High-performance combinatorial computing is an infant field, in sharp contrast with numerical scientific computing. We argue that many of the tools of high-performance numerical computing - in particular, parallel algorithms and data structures for computation with sparse matrices - can form the nucleus of a robust infrastructure for parallel computing on graphs. We demonstrate this with an implementation of a graph analysis benchmark using the sparse matrix infrastructure in Star-P, our parallel dialect of the MATLAB programming language.

Standards for graph algorithm primitives

It is our view that the state of the art in constructing a large collection of graph algorithms in terms of linear algebraic operations is mature enough to support the emergence of a standard set of primitive building blocks. This paper is a position paper defining the problem and announcing our intention to launch an open effort to define this standard.

Scalable complex graph analysis with the knowledge discovery toolbox

The Knowledge Discovery Toolbox (KDT) enables domain experts to perform complex analyses of huge datasets on supercomputers using a high-level language without grappling with the difficulties of writing parallel code, calling parallel libraries, or becoming a graph expert. KDT delivers competitive performance from a general-purpose, reusable library for graphs on the order of 10 billion edges and greater. We describe our approach for supporting arbirary vertex and edge attributes, in-place graph filtering, and graph traversal using pre-defined access patterns.

Extending SPARQL with graph functions

Much of the early domain-specific success with graph analytics has been with algorithms whose results are based on global graph structure. An example of such an algorithm is betweenness centrality, whose value for any vertex potentially depends on the number of shortest paths between all pairs of vertices in the entire graph. YarcDatas UrikaTM customers use SPARQLs graph-oriented pattern-matching capabilities, but many of them also require a capability to call graph functions such as betweenness centrality. This customer feedback led us to combine SPARQL 1.1s query capabilities with classical and emerging graph-analytic algorithms (e.g., community detection, shortest path, betweenness, BadRank). With this capability, a SPARQL query can select a specific subgraph of interest, pass that subgraph to a graph algorithms for deep analysis, and then pass those results back to an enclosing SPARQL query that post-processes those results as needed. With the Summer 2014 Urika release, we have extended the SPARQL implementation with a graph-function capability and a small set of built-in graph functions. We describe our design approach and our experiences with this first release, including anecdotal evidence of dramatically higher performance. Built-in graph functions represent an important step in the maturation of graph analysis and SPARQL. As common motifs emerge from use cases, those motifs may be mapped to specific graph functions that can be highly tuned for much higher performance than will be possible for SPARQL. Identifying those motifs and developing the underlying graph functions to accelerate their execution is a topic of intense effort industry-wide. Graph functions merged with SPARQL provide a new mechanism by which third-party graph-algorithm developers may expose their algorithms to widespread use.

An Interactive Environment to Manipulate Large Graphs

Interactive environments such as Matlab and Star-P have made numerical computing tremendously accessible to engineers and scientists. They allow people who are not well-versed in the art of numerical computing to nonetheless reap the benefits of numerical computing. The same is not true in general for combinatorial computing. Often, many interesting problems require a mix of numerical and combinatorial computing. Tools developed for numerical computing - such as sparse matrix algorithms - can also be used to develop a comprehensive infrastructure for graph algorithms. We describe the current status of our effort to build a comprehensive infrastructure for operations on large graphs in an interactive parallel environment such as Star-P.

Distributed Sparse Matrices for Very High Level Languages

Abstract Sparse matrices are first-class objects in many VHLLs (very high-level languages) that are used for scientific computing. They are a basic building block for various numerical and combinatorial algorithms. Parallel computing is becoming ubiquitous, specifically due to the advent of multi-core architectures. As existing VHLLs are adapted to emerging architectures, and new ones are conceived, one must rethink about trade-offs in language design. We describe the design and implementation of a sparse matrix infrastructure for Star -P, a parallel implementation of the Matlab ® programming language. We demonstrate the versatility of our infrastructure by using it to implement a benchmark that creates and manipulates large graphs. Our design is by no means specific to Star -P—we hope it will influence the design of sparse matrix infrastructures in other languages.