Let iT be a bipartite graph with bipartition (A, B) where \A\-n and every subset X of A with at most a n elements has at least b\X\ neighbors (o 1). We consider the problem of computing a matching from a given subset...
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In this paper we study the overheads arising in our algorithm for distributed evaluation of Min/Max trees. the overheads are classified into search overhead, performance loss, and decrease of work load. Several mechan...
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the proceedings contain 43 papers. the topics discussed include: publish and perish: definition and analysis of an n-person publication impact game;exponential separation of quantum and classical online space complexi...
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ISBN:
(纸本)1595934529
the proceedings contain 43 papers. the topics discussed include: publish and perish: definition and analysis of an n-person publication impact game;exponential separation of quantum and classical online space complexity;minimizing the stretch when scheduling flows of biological requests;position paper and brief announcement: the FG programming environment - good and good for you;efficient parallelalgorithms for dead sensor diagnosis and multiple access channels;on the communication complexity of randomized broadcasting in random-like graphs;strip packing with precedence constraints and strip packing with release times;on space-stretch trade-offs: lower bounds;a performance analysis of local synchronization;the cache complexity of multithreaded cache oblivious algorithms;and deterministic load balancing and dictionaries in the parallel disk model.
Given a set of n nuts of distinct widths and a set of n bolts such that each nut corresponds to a unique bolt of the same width, how should we match every nut with its corresponding bolt by comparing nuts with bolts? ...
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Given a set of n nuts of distinct widths and a set of n bolts such that each nut corresponds to a unique bolt of the same width, how should we match every nut with its corresponding bolt by comparing nuts with bolts? (No comparison is allowed between two nuts or two bolts.) the problem can be naturally viewed as a variant of the classic sorting problem as follows. Given two lists of n numbers each such that one list is a permutation of the other, how should we sort the lists by comparisons only between numbers in different lists? We give an O(n log n)-time deterministic algorithm for the problem. this is optimal up to a constant factor and answers an open question posed by Alon et al. [proceedings of the 5thannualacm-SIAM symposium on Discrete algorithms, 1994, pp. 690-696]. Moreover, when copies of nuts and bolts are allowed, our algorithm runs in optimal O(log n) time on n processors in Valiant's parallel comparison tree model. Our algorithm is based on the AKS sorting algorithm with substantial modifications.
the parallel derivative of a set of strings is introduced. Given a serial, repetition-free parallel program schema, its closure is constructed by taking parallel derivatives of its set of computations. the constructio...
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A quantitative comparison of the BSP and LogP models for parallel computation is developed. Very efficient cross simulations between the two models are derived, showing their substantial equivalence for algorithmic de...
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ISBN:
(纸本)9780897918091
A quantitative comparison of the BSP and LogP models for parallel computation is developed. Very efficient cross simulations between the two models are derived, showing their substantial equivalence for algorithmic design guided by asymptotic analysis. It is also shown that the two models can be implemented with similar performance on most point-to-point networks. In conclusion, within the limits of our analysis that is mainly of asymptotic nature, BSP and LogP can be viewed as closely related variants within the bandwidth-latency framework for modeling parallel computation. BSP seems somewhat preferable due to greater simplicity and portability, and slightly greater power.
In a breakthrough result, Spielman and Teng (2004) developed a nearly-linear time solver for Laplacian linear equations, i.e. equations where the coefficient matrix is symmetric with non-negative diagonals and zero ro...
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ISBN:
(纸本)9798400704161
In a breakthrough result, Spielman and Teng (2004) developed a nearly-linear time solver for Laplacian linear equations, i.e. equations where the coefficient matrix is symmetric with non-negative diagonals and zero rowsums. Since the development of the Spielman-Teng solver, there has been substantial progress, simplifying and improving their result, but obtaining a fast practical, parallel Laplacian solver remains an open problem. We present a framework for obtaining extremely simple, parallel Laplacian linear equation solvers with nearly-linear work and sub-linear depth. Our framework allows us to parallelize any Laplacian solver based on repeated single-vertex approximate Gaussian elimination. We demonstrate this by parallelizing boththe algorithm of Kyng and Sachdeva (2016) and the practical variant by Gao, Kyng, and Spielman (2023). Our framework is work-efficient in the sense of matching the sequential work of these algorithms. Our parallelization framework is very simple: We sample a subset of the current low-degree vertices (sparse columns), and in parallel we eliminate all vertices that are isolated in the resulting induced subgraph. this approach can be combined with any parallelizable approximate single-vertex elimination subroutine with sparse output. Given the simplicity of the approach, we believe that using it to parallelize the solver of Gao, Kyng, and Spielman (2023) is the most promising direction for obtaining practical parallel Laplacian solvers. If we additionally use a parallel spectral sparsification routine, our approach can be modified to work in polylogarithmic depth and nearly-linear work.
We present lower bounds for time needed to solve basic problems on three general-purpose models of parallel computation: the shared-memory models QSM and s-QSW, and the distributed-memory model, the BSP. For each of t...
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ISBN:
(纸本)9780897919890
We present lower bounds for time needed to solve basic problems on three general-purpose models of parallel computation: the shared-memory models QSM and s-QSW, and the distributed-memory model, the BSP. For each of these models, we also obtain lower bounds for the number of rounds needed to solve these problems using a randomized algorithm on a p-processor machine. Our results on 'rounds' is of special interest in the context of designing work-efficient algorithms on a machine where latency and synchronization costs are high. Many of our lower bound results are complemented by upper bounds that match the lower bound or are close to it.
the proceedings contain 42 papers. the topics discussed include: on dynamic bin packing for resource allocation in the cloud;on the online fault-tolerant server consolidation problem;on computing maximal independent s...
ISBN:
(纸本)9781450328210
the proceedings contain 42 papers. the topics discussed include: on dynamic bin packing for resource allocation in the cloud;on the online fault-tolerant server consolidation problem;on computing maximal independent sets of hypergraphs in parallel;simple parallel and distributed algorithms for spectral graph sparsification;concurrent data structures for efficient streaming aggregation;provably good scheduling for parallel programs that use data structures through implicit batching;scheduling selfish jobs on multidimensional parallel machines;LP rounding and combinatorial algorithms for minimizing active and busy time;a note on multiprocessor speed scaling with precedence constraints;executing dynamic data-graph computations deterministically using chromatic scheduling;the PCL theorem. transactions cannot be parallel, consistent and live;adaptive integration of hardware and software lock elision techniques;and transaction-friendly condition variables.
this paper envisions an extension to a standard instruction set which efficiently implements PRAM-style algorithms using explicit multi-threaded instruction-level parallelism (ILP);that is, Explicit Multi-threading (X...
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ISBN:
(纸本)9780897919890
this paper envisions an extension to a standard instruction set which efficiently implements PRAM-style algorithms using explicit multi-threaded instruction-level parallelism (ILP);that is, Explicit Multi-threading (XMT), a fine-grained computational paradigm covering the spectrum from algorithmsthrough architecture to implementation is introduced;new elements are added where needed.
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