This paper presents the design and analysis of parallel approximation algorithms for facility-location problems, including NC and RNC algorithms for (metric) facility location, k-center, k-median, and k-means These pr...
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ISBN:
(纸本)9781450300797
This paper presents the design and analysis of parallel approximation algorithms for facility-location problems, including NC and RNC algorithms for (metric) facility location, k-center, k-median, and k-means These problems have received considerable attention during the past decades from the approximation algorithms community, which primarily concentrates on improving the approximation guarantees In this paper, we ask. Is it possible to parallelize some of the beautiful results from the sequential setting? Our starting point is a small, but diverse, subset of results in approximation algorithms for facility-location problems, with a primary goal of developing techniques for devising their efficient parallel counterparts. We focus on giving algorithms with low depth, near work efficiency (compared to the sequential versions), and low cache complexity
We prove a number of negative results about practical (i.e., numerically accurate) algorithms for certain matrix factorizations. In particular, we prove that the popular Givens' method for computing the QR decompo...
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ISBN:
(纸本)9780897918909
We prove a number of negative results about practical (i.e., numerically accurate) algorithms for certain matrix factorizations. In particular, we prove that the popular Givens' method for computing the QR decomposition is inherently sequential over the realistic model of floating point arithmetic. We also prove a number of additional results concerning Gaussian Elimination for computing the LU decomposition. Altogether, the results of this paper support the widespread belief that there is a tradeoff between parallelism and accuracy in numerical algorithms.
A library, called PAD, of basic parallelalgorithms and data structures for the PRAM is currently being implemented using the PRAM programming language Fork95. Main motivations of the PAD project is to study the PRAM ...
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A library, called PAD, of basic parallelalgorithms and data structures for the PRAM is currently being implemented using the PRAM programming language Fork95. Main motivations of the PAD project is to study the PRAM as a practical programming model, and to provide an organized collection of basic PRAM algorithms for the SB-PRAM under completion at the University of Saarbruecken. We give a brief survey of Fork95, and describe the main components of PAD. Finally we report on the status of the language and library and discuss further developments.
Scheduling problems that are critical and prevalent in practical parallel computing are computed. A polynomial time makespan algorithm that produces a schedule of length O(V+Φ log T), which is therefore an O(log T) a...
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ISBN:
(纸本)9780897918091
Scheduling problems that are critical and prevalent in practical parallel computing are computed. A polynomial time makespan algorithm that produces a schedule of length O(V+Φ log T), which is therefore an O(log T) approximation is presented to solve these problems. The makespan algorithm can be extended to minimize the weighted average completion time over all the jobs to the same approximation factor of O(log T).
作者：
Koo, JaehyunMIT
77 Massachusetts Ave Cambridge MA 02139 USA
We present an O(1)-round fully-scalable deterministic massively parallel algorithm for computing the min-plus matrix multiplication of unit-Monge matrices. We use this to derive a O(log n)-round fully-scalable massive...
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ISBN:
(纸本)9798400704161
We present an O(1)-round fully-scalable deterministic massively parallel algorithm for computing the min-plus matrix multiplication of unit-Monge matrices. We use this to derive a O(log n)-round fully-scalable massively parallel algorithm for solving the exact longest increasing subsequence (LIS) problem. For a fully-scalable MPC regime, this result substantially improves the previously known algorithm of O(log(4) n)-round complexity, and matches the best algorithm for computing the (1 + epsilon)-approximation of LIS.
Diffusive schemes have been widely analyzed for parallel and distributed load balancing. It is well known that their convergence rates depend on the eigenvalues of some associated matrices and on the expansion propert...
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Diffusive schemes have been widely analyzed for parallel and distributed load balancing. It is well known that their convergence rates depend on the eigenvalues of some associated matrices and on the expansion properties of the underlying graphs. In the first part of this paper we make use of these relationships in order to obtain new spectral bounds on the edge and node expansion of graphs. We show that these new bounds are better than the classical bounds for several graph classes. In the second part of the paper, we consider the load balancing problem for indivisible unit size tokens. Since known diffusion schemes do not completely balance the load for such settings, we propose a randomized distributed algorithm based on Markov chains to reduce the load imbalance. We prove that this approach provides the best asymptotic result that can be achieved in l1- or l2-norm concerning the final load situation.
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