The Grid 2: Blueprint for a New Computing Infrastructure

Journal of the ACM

Greedy algorithms are practitioners’ best friends—they are intuitive, are simple to implement, and often lead to very good solutions. However, implementing greedy algorithms in a distributed setting is challenging since the greedy choice is inherently sequential, and it is not clear how to take advantage of the extra processing power. Our main result is a powerful sampling technique that aids in parallelization of sequential algorithms. Armed with this primitive, we then adapt a broad class of greedy algorithms to the MapReduce paradigm; this class includes maximum cover and submodular maximization subject to p-system constraint problems. Our method yields efficient algorithms that run in a logarithmic number of rounds while obtaining solutions that are arbitrarily close to those produced by the standard sequential greedy algorithm. We begin with algorithms for modular maximization subject to a matroid constraint and then extend this approach to obtain approximation algorithms for submodular maximization subject to knapsack or p-system constraints.

Fast Greedy Algorithms in MapReduce and Streaming

https://people.seas.harvard.edu/%7Evaliant/bridging-2010.pdf

A bridging model for multi-core computing

Triangle counting and enumeration has emerged as a basic tool in large-scale network analysis, fueling the development of algorithms that scale to massive graphs. Most of the existing algorithms, however, are designed for the distributed-memory setting or the external-memory setting, and cannot take full advantage of a multicore machine, whose capacity has grown to accommodate even the largest of real-world graphs.

/pdf/multicore-triangle-computations-without-tuning-4ij4hixctk.pdf

Multicore triangle computations without tuning

Tensor Core Units (TCUs) are hardware accelerators developed for deep neural networks, which efficiently support the multiplication of two dense $\sqrt{m}\times \sqrt{m}$ matrices, where m is a given hardware parameter. In this paper, we show that TCUs can speed up similarity search problems as well. We propose algorithms for the Johnson-Lindenstrauss dimensionality reduction and for similarity join that, by leveraging TCUs, achieve a $\varOmega (\sqrt{m})$ speedup up with respect to traditional approaches.

Similarity Search with Tensor Core Units

An Optimized Data Structure for High Throughput 3D Proteomics Data: mzRTree

On the limits of cache-oblivious rational permutations

A common approach in the design of MapReduce algorithms is to minimize the number of rounds. Indeed, there are many examples in the literature of monolithic MapReduce algorithms, which are algorithms requiring just one or two rounds. However, we claim that the design of monolithic algorithms may not be the best approach in cloud systems. Indeed, multi-round algorithms may exploit some features of cloud platforms by suitably setting the round number according to the execution context. In this paper we carry out an experimental study of multi-round MapReduce algorithms aiming at investigating the performance of the multi-round approach. We use matrix multiplication as a case study. We first propose a scalable Hadoop library, named M$_3$, for matrix multiplication in the dense and sparse cases which allows to tradeoff round number with the amount of data shuffled in each round and the amount of memory required by reduce functions. Then, we present an extensive study of this library on an in-house cluster and on Amazon Web Services aiming at showing its performance and at comparing monolithic and multi-round approaches. The experiments show that, even without a low level optimization, it is possible to design multi-round algorithms with a small running time overhead.

Experimental Evaluation of Multi-Round Matrix Multiplication on MapReduce

We consider the well-known problem of enumerating all triangles of an undirected graph. Our focus is on determining the input/output (I/O) complexity of this problem. Let $E$ be the number of edges, $M 0$. Our results are based on a new color coding technique, which may be of independent interest.

Francesco Silvestri

Papers

Similarity Search with Tensor Core Units

An Optimized Data Structure for High Throughput 3D Proteomics Data: mzRTree

On the limits of cache-oblivious rational permutations

Experimental Evaluation of Multi-Round Matrix Multiplication on MapReduce

The Input/Output Complexity of Triangle Enumeration