Fast Inner Product Computation on Short Buses

We propose a VLSI inner product processor architecture involving broadcasting only over short buses (containing less than 64 switches). The architecture leads to an efficient algorithm for the inner product computation. Specifically, it takes 13 broadcasts, each over less than 64 switches, plus 2 carry-save additions (tcsa) and 2 carry-lookahead additions (tcla) to compute the inner product of two arrays of N = 29 elements, each consisting of m = 64 bits. Using the same order of VLSI area, our algorithm runs faster than the best known fast inner product algorithm of Smith and Torng [ Design of a fast inner product processor, Proceedings of IEEE 7th Symposium on Computer Arithmetic (1985)], which takes about 28 tcsa + tcla for the computation

Efficient parallel computation on multiprocessors with optical interconnection networks

This dissertation studies optical interconnection networks, their architecture, address schemes, and computation and communication capabilities. We focus on a simple but powerful optical interconnection network model - the Linear Array with Reconfigurable pipelined Bus System (LARPBS). We extend the LARPBS model to a simplified higher dimensional LAPRBS and provide a set of basic computation operations. We then study the following two groups of parallel computation problems on both one dimensional LARPBS\u27s as well as multi-dimensional LARPBS\u27s: parallel comparison problems, including sorting, merging, and selection; Boolean matrix multiplication, transitive closure and their applications to connected component problems. We implement an optimal sorting algorithm on an n-processor LARPBS. With this optimal sorting algorithm at disposal, we study the sorting problem for higher dimensional LARPBS\u27s and obtain the following results: • An optimal basic Columnsort algorithm on a 2D LARPBS. • Two optimal two-way merge sort algorithms on a 2D LARPBS. • An optimal multi-way merge sorting algorithm on a 2D LARPBS. • An optimal generalized column sort algorithm on a 2D LARPBS. • An optimal generalized column sort algorithm on a 3D LARPBS. • An optimal 5-phase sorting algorithm on a 3D LARPBS. Results for selection problems are as follows: • A constant time maximum-finding algorithm on an LARPBS. • An optimal maximum-finding algorithm on an LARPBS. • An O((log log n)2) time parallel selection algorithm on an LARPBS. • An O(k(log log n)2) time parallel multi-selection algorithm on an LARPBS. While studying the computation and communication properties of the LARPBS model, we find Boolean matrix multiplication and its applications to the graph are another set of problem that can be solved efficiently on the LARPBS. Following is a list of results we have obtained in this area. • A constant time Boolean matrix multiplication algorithm. • An O(log n)-time transitive closure algorithm. • An O(log n)-time connected components algorithm. • An O(log n)-time strongly connected components algorithm. The results provided in this dissertation show the strong computation and communication power of optical interconnection networks

BFS-4K: an Efficient Implementation of BFS for Kepler GPU Architectures

Breadth-first search (BFS) is one of the most common graph traversal algorithms and the building block for a wide range of graph applications. With the advent of graphics processing units (GPUs), several works have been proposed to accelerate graph algorithms and, in particular, BFS on such many-core architectures. Nevertheless, BFS has proven to be an algorithm for which it is hard to obtain better performance from parallelization. Indeed, the proposed solutions take advantage of the massively parallelism of GPUs but they are often asymptotically less efficient than the fastest CPU implementations. This article presents BFS-4K, a parallel implementation of BFS for GPUs that exploits the more advanced features of GPU-based platforms (i.e., NVIDIA Kepler) and that achieves an asymptotically optimal work complexity.The article presents different strategies implemented in BFS-4K to deal with the potential workload imbalance and thread divergence caused by any actual graph non-homogeneity.The article presents the experimental results conducted on several graphs of different size and characteristics to understand how the proposed techniques are applied and combined to obtain the best performance from the parallel BFS visits. Finally, an analysis of the most representative BFS implementations for GPUs at the state of the art and their comparison with BFS-4K are reported to underline the efficiency of the proposed solution