arXiv subjects

John R. Gilbert

Publications and source records attributed to John R. Gilbert.

5 recordsLinked to original sources

arXiv2021

Combinatorial BLAS 2.0: Scaling combinatorial algorithms on distributed-memory systems

Combinatorial algorithms such as those that arise in graph analysis, modeling of discrete systems, bioinformatics, and chemistry, are often hard to parallelize. The Combinatorial BLAS library implements key computational primitives for rapid development of combinatorial algorithms in distributed-memory systems. During the decade since its first introduction, the Combinatorial BLAS library has evolved and expanded significantly. This paper details many of the key technical features of Combinatorial BLAS version 2.0, such as communication avoidance, hierarchical parallelism via in-node multithreading, accelerator support via GPU kernels, generalized semiring support, implementations of key data structures and functions, and scalable distributed I/O operations for human-readable files. Our paper also presents several rules of thumb for choosing the right data structures and functions in Combinatorial BLAS 2.0, under various common application scenarios.

cs.DC↗

arXiv2017

LiRa: A New Likelihood-Based Similarity Score for Collaborative Filtering

Recommender system data presents unique challenges to the data mining, machine learning, and algorithms communities. The high missing data rate, in combination with the large scale and high dimensionality that is typical of recommender systems data, requires new tools and methods for efficient data analysis. Here, we address the challenge of evaluating similarity between two users in a recommender system, where for each user only a small set of ratings is available. We present a new similarity score, that we call LiRa, based on a statistical model of user similarity, for large-scale, discrete valued data with many missing values. We show that this score, based on a ratio of likelihoods, is more effective at identifying similar users than traditional similarity scores in user-based collaborative filtering, such as the Pearson correlation coefficient. We argue that our approach has significant potential to improve both accuracy and scalability in collaborative filtering.

cs.IR↗

arXiv2016

An Empirical Study of Cycle Toggling Based Laplacian Solvers

We study the performance of linear solvers for graph Laplacians based on the combinatorial cycle adjustment methodology proposed by [Kelner-Orecchia-Sidford-Zhu STOC-13]. The approach finds a dual flow solution to this linear system through a sequence of flow adjustments along cycles. We study both data structure oriented and recursive methods for handling these adjustments. The primary difficulty faced by this approach, updating and querying long cycles, motivated us to study an important special case: instances where all cycles are formed by fundamental cycles on a length $n$ path. Our methods demonstrate significant speedups over previous implementations, and are competitive with standard numerical routines.

cs.DS↗

arXiv2015

Evaluating the Potential of a Dual Randomized Kaczmarz Solver for Laplacian Linear Systems

A new method for solving Laplacian linear systems proposed by Kelner et al. involves the random sampling and update of fundamental cycles in a graph. Kelner et al. proved asymptotic bounds on the complexity of this method but did not report experimental results. We seek to both evaluate the performance of this approach and to explore improvements to it in practice. We compare the performance of this method to other Laplacian solvers on a variety of real world graphs. We consider different ways to improve the performance of this method by exploring different ways of choosing the set of cycles and the sequence of updates, with the goal of providing more flexibility and potential parallelism. We propose a parallel model of the Kelner et al. method, for evaluating potential parallelism in terms of the span of edges updated at each iteration. We provide experimental results comparing the potential parallelism of the fundamental cycle basis and our extended cycle set. Our preliminary experiments show that choosing a non-fundamental set of cycles can save significant work compared to a fundamental cycle basis.

cs.DS↗

arXiv2010

Highly Parallel Sparse Matrix-Matrix Multiplication

Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an unbounded number of processors. Our algorithms are based on two-dimensional block distribution of sparse matrices where serial sections use a novel hypersparse kernel for scalability. We give a state-of-the-art MPI implementation of one of our algorithms. Our experiments show scaling up to thousands of processors on a variety of test scenarios.

cs.DC↗