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On the parallel complexity of integer programming 89

On the parallel complexity of integer programming

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1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Deng, Xiaotie Dept. of Operations Research Stanford University United States Dept. of Computer Science and Engineering UC at San Diego United States

ISBN: (纸本)089791323X

We show that the several problems, whose complexity with respect P and NC was open, are equivalent under NC-reductions. These include: (1) Finding the optimal solution of a two-variable integer program;(2) Determining whether a set of linear inequalities in two dimensions has all integer solution;(3) Finding all intermediate results in the Euclidean algorithm for the greatest common divisor of two integers;(4) Finding integers x and y that minimize mx+ny > 0 (as is well known, the result mx+ny is the greatest common divisor of m and n). We also show that integer programming can be NC-reduced to the basis reduction problem (and tiffs holds in any fixed dimension). Thus, basis reduction is the only step in Lenstra's algorithm that is not easily parallelizable. © 1989 acm.

关键词： Integer programming

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Space-efficient representations of shared data for parallel computers 90

Space-efficient representations of shared data for parallel ...

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SPAA '90 - proceedings of the 2nd annual acm symposium on parallel algorithms and architectures

作者： Herley, Kieran T. Cornell Univ Itaca NY United States

ISBN: (纸本)0897913701

The problem of representing a set U = {u1, ..., um} of read-write variables on an n-node distributed memory parallel computer is considered. It is shown that U can be represented among the n nodes of a variant of the mesh-of-trees using O((m/n)polylog(m/n)) storage per node such that any n-tuple of variables may be accessed in O(log n(log log n)2) time in the worst case for m polynomial in n.

关键词： Computer systems, Digital

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Efficient disk allocation for fast similarity searching 98

Efficient disk allocation for fast similarity searching

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proceedings of the 1998 10th annual acm symposium on parallel algorithms and architectures, SPAA

作者： Prabhakar, S. Agrawal, D. El Abbadi, A. Univ of California Santa Barbara CA United States

ISBN: (纸本)9780897919890

As databases increasingly integrate non-textual information it is becoming necessary to support efficient similarity searching in addition to range searching. Recently, declustering techniques have been proposed for improving the performance of similarity searches through parallel I/O. In this paper, we propose a new scheme which provides good declustering for similarity searching. In particular, it does global declustering as opposed to local declustering, exploits the availability of extra disks and does not limit the partitioning of the data space. Our technique is based upon the Cyclic declustering schemes which were developed for range and partial match queries. We establish, in general, that Cyclic declustering techniques outperform previously proposed techniques.

关键词： parallel algorithms

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Framework for simple sorting algorithms on parallel disk systems

Framework for simple sorting algorithms on parallel disk sys...

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proceedings of the 1998 10th annual acm symposium on parallel algorithms and architectures, SPAA

作者： Rajasekaran, S. Univ of Florida Gainesville United States

In this paper we present a simple parallel sorting algorithm and illustrate two applications. The algorithm (called the (l, m)-merge sort (LMM)) is an extension of the bitonic and odd-even merge sorts. Literature on parallel sorting is abundant. Many of the algorithms proposed, though being theoretically important, may not perform satisfactorily in practice owing to large constants in their time bounds. The algorithm to be presented in this paper, due partly to its simplicity, results in small constants. We present an implementation for the parallel disk sorting problem. The algorithm is asymptotically optimal (assuming that N is a polynomial in M, where N is the number of records to be sorted and M is the internal memory size). The underlying constant is very small. This algorithm has a better performance than the disk-striped mergesort (DSM) algorithm when the number of disks is large. Our implementation is as simple as that of DSM (requiring no fancy data structures or prefetch techniques). As a second application, we prove that we can get a sparse enumeration sort on the hypercube that is simpler than that of the classical algorithm of Nassimi and Sahni. We also show that Leighton's columnsort algorithm is a special case of LMM.

关键词： parallel algorithms

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Fast set operations using treaps 98

Fast set operations using treaps

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proceedings of the 1998 10th annual acm symposium on parallel algorithms and architectures, SPAA

作者： Blelloch, G.E. Reid-Miller, M. Carnegie Mellon Univ Pittsburgh PA United States

ISBN: (纸本)9780897919890

We present parallel algorithms for union, intersection and difference on ordered sets using random balanced binary trees (treaps [26]). For two sets of size n and m (m ≤ n) the algorithms run in expected O(m lg(n/m)) work and O(lg n) depth (parallel time) on an EREW PRAM with scan operations (implying O(lg2 n) depth on a plain EREW PRAM). As with the sequential algorithms on treaps for insertion and deletion the main advantage of our algorithms are their simplicity. In fact our algorithms for set operations seem simpler than previous sequential algorithms with the same work bounds, and might therefore also be useful in a sequential context. To analyze the effectiveness of the algorithms we implemented both sequential and parallel versions of the algorithms and ran several experiments on them. Our parallel implementation uses the Cilk [5] shared memory runtime system on a 16 processor SGI Power Challenge and a 6 processor Sun Ultra Enterprise 3000. It shows reasonable speedup: 6.3 to 6.8 speedup on 8 processors of the SGI, and 4.1 to 4.4 speedup on 5 processors of the Sun.

关键词： parallel algorithms

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A Simpler and parallelizable O(√log n)-approximation Algorithm for SPARSEST CUT 24

A Simpler and Parallelizable O(√log n)-approximation Algori...

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36th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Kolmogorov, Vladimir Inst Sci & Technol Austria ISTA Klosterneuburg Austria

ISBN: (纸本)9798400704161

Currently, the best known tradeoff between approximation ratio and complexity for the Sparsest Cut problem is achieved by the algorithm in [Sherman, FOCS 2009]: it computes O(root(log n)/epsilon)-approximation using O(n(epsilon) log(O(1))n) maxflows for any epsilon is an element of[Theta(1/log n), Theta(1)]. It works by solving the SDP relaxation of [Arora-Rao-Vazirani, STOC 2004] using the Multiplicative Weights Update algorithm (MW) of [Arora-Kale, Jacm 2016]. To implement one MW step, Sherman approximately solves a multicommodity flow problem using another application of MW. Nested MW steps are solved via a certain "chaining" algorithm that combines results of multiple calls to the maxflow algorithm. We present an alternative approach that avoids solving the multicommodity flow problem and instead computes "violating paths". This simplifies Sherman's algorithm by removing a need for a nested application of MW, and also allows parallelization: we show how to compute O(root(log n)/epsilon)-approximation via O(log(O(1)) n) maxflows using O(n(epsilon)) processors. We also revisit Sherman's chaining algorithm, and present a simpler version together with a new analysis.

关键词： SPARSEST CUT approximation algorithms parallel algorithms

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annual acm symposium on parallelism in algorithms and architectures

Annual ACM Symposium on Parallelism in Algorithms and Archit...

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28th acm symposium on parallelism in algorithms and architectures, SPAA 2016

ISBN: (纸本)9781450342100

The proceedings contain 52 papers. The topics discussed include: randomized approximate nearest neighbor search with limited adaptivity;encoding short ranges in TCAM without expansion: efficient algorithm and applications;extending the nested parallel model to the nested dataflow model with provably efficient schedulers;latency-hiding work stealing: scheduling interacting parallel computations with work stealing;provably good and practically efficient parallel race detection for fork-join programs;dynamic determinacy race detection for task parallelism with futures;RUBIC: online parallelism tuning for co-located transactional memory applications;investigating the performance of hardware transactions on a multi-socket machine;parallel algorithms for asymmetric read-write costs;general profit scheduling and the power of migration on heterogeneous machines;the power of migration in online machine minimization;fair online scheduling for selfish jobs on heterogeneous machines;scheduling parallelizable jobs online to minimize the maximum flow time;clairvoyant dynamic bin packing for job scheduling with minimum server usage time;parallel equivalence class sorting: algorithms, lower bounds, and distribution-based analysis;and parallel approaches to the string matching problem on the GPU.

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SPAA'07: proceedings of the Nineteenth annual symposium on parallelism in algorithms and architectures

SPAA'07: Proceedings of the Nineteenth Annual Symposium on P...

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SPAA'07: 19th annual symposium on parallelism in algorithms and architectures

ISBN: (纸本)159593667X

The proceedings contain 37 papers. The topics discussed include: on triangulation of simple networks;strong-diameter decompositions of minor free graphs;approximation algorithms for multiprocessor scheduling under uncertainty;scheduling DAGs on asynchronous processors;scheduling to minimize gaps and power consumption;cache-oblivious streaming B-trees;an experimental comparison of cache-oblivious and cache-conscious programs;scheduling threads for constructive cache sharing on CMPs;proximity-aware directory-based coherence for multi-core processor architectures;a parallel dynamic programming algorithm on a multi-core architecture;tight bounds for distributed selection;local MST computation with short advice;distributed approximation of capacitated dominating sets;packing to angles and sectors;and the notion of a timed register and its application to indulgent synchronization.

关键词： Computer programming

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SPAA'09 - proceedings of the 21st annual symposium on parallelism in algorithms and architectures

SPAA'09 - Proceedings of the 21st Annual Symposium on Parall...

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21st annual symposium on parallelism in algorithms and architectures, SPAA'09

ISBN: (纸本)9781605586069

The proceedings contain 43 papers. The topics discussed include: speed scaling of processes with arbitrary speedup curves on a multiprocessor;the bell is ringing in speed-scaled multiprocessor scheduling;mapping filtering streaming applications with communication costs;scheduling to minimize staleness and stretch in real-time data warehouses;parameterized maximum and average degree approximation in topic-based publish-subscribe overlay network design;selfishness in transactional memory;at-most-once semantics in asynchronous shared memory;memory models: a case for rethinking parallel languages and hardware;the life and times of a ZooKeeper;Cassandra - a structured storage system on a P2P network;Pregel: a system for large-scale graph processing;towards transactional memory semantics for C++;on avoiding spare aborts in transactional memory;inherent limitations on disjoint-access parallel implementations of transactional memory;reducers and other Cilk++ hyperobjects;and beyond nested parallelism: tight bounds on work-stealing overheads for parallel futures.

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Inherent Limitations on Disjoint-Access parallel Implementations of Transactional Memory (Preliminary Version) 09

Inherent Limitations on Disjoint-Access Parallel Implementat...

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21st acm symposium on parallelism in algorithms and architectures

作者： Attiya, Hagit Hillel, Eshcar Milani, Alessia Technion Israel Inst Technol Dept Comp Sci IL-32000 Haifa Israel

ISBN: (纸本)9781605586069

Transactional memory (TM) is a promising approach for designing concurrent data structures, and it is essential to develop better understanding of the formal properties that can be achieved by TM implementations. Two fundamental properties of TM implementations are disjoint-access parallelism, which is critical for their scalability, and the invisibility of read operations, which reduces memory contention. This paper proves an inherent tradeoff for implementations of transactional memories: they cannot be both disjoint-access parallel and have read-only transactions that are invisible and always terminate successfully. In fact, a lower bound of Omega(t) is proved on the number of writes needed in order to implement a read-only transaction of t items, which successfully terminates in a disjoint-access parallel TM implementation. The results assume strict serializability and thus hold under the assumption of opacity. It is shown how to extend the results to hold also for weaker consistency conditions, serializability and snapshot isolation.

关键词： Transactional memory disjoint-access parallelism partial snapshots lower bound impossibility result

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