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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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parallel algorithms for generating random permutations on a shared memory machine 90

Parallel algorithms for generating random permutations on a ...

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

作者： Anderson, Richard J. Univ of Washington WA United States

ISBN: (纸本)0897913701

In this paper we consider the problem of generating random permutations on small parallel machines. The machines that we have in mind are shared memory machines with a constant number of processors such as the Sequent Symmetry. We describe a parallel implementation of the 'shuffling' algorithm for generating a random permutation. If the hardware operates in a fair manner, this algorithm generates a fully random permutation. However, if the machine resolves contention in a malicious manner, then the algorithm does not generate permutations uniformly. We give almost tight bounds on the degree that an adversary can reduce the randomness. We also discuss the cost of locking data in the algorithm and present a method of generating random permutations with substantially reduced locking cost.

关键词： Computer programming

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parallel construction of trees with optimal weighted path length 91

Parallel construction of trees with optimal weighted path le...

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3rd annual acm symposium on parallel algorithms and architectures, SPAA 1991

作者： Larmore, Lawrence L. Przytycka, Teresa M. Department of Computer Science University of California RiversideCA92521 United States Instytut Informatyki Uniwersytet Warszawski United States

ISBN: (纸本)0897914384

This paper deals with the problem of parallel construction of trees with optimal weighted path length. We study both the unordered case, known as the Huffman coding problem and the ordered case known as the optimal alphabetic binary tree problem. The methods used in both cases are different. We reduce the Huffman coding problem to the Concave Least Weight Subsequence and give a parallel algorithm that solves the latter problem in O(√n log n) time with n processors on a CREW PRAM. This leads to the first sublinear time o(n2)-total work parallel algorithm for the Huffman coding problem. The alphabetic binary tree problem is a special case of the Optimum Binary Search Tree problem and can be solved in O(log2 n) time with n4 processors using the dynamic programming technique. We show that an optimal height restricted alphabetic tree can be constructed in O(L log n) time on a CREW PRAM using only linearly many processors, where L is an upper bound on the height of the tree. © 1991 acm.

关键词： parallel algorithms

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A parallel Dynamic Programming Algorithm on a Multi-core Architecture 07

A Parallel Dynamic Programming Algorithm on a Multi-core Arc...

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19th annual symposium on parallelism in algorithms and architectures

作者： Tan, Guangming Sun, Ninghui Gao, Guang R. Chinese Acad Sci Key Lab Comp Syst & Architecture Beijing Peoples R China

ISBN: (纸本)9781595936677

Dynamic programming is an efficient technique to solve combinatorial search and optimization problem. There have been many parallel dynamic programming algorithms. The purpose of this paper is to study a family of dynamic programming algorithm where data dependence appear between non-consecutive stages, in other words, the data dependence is non-uniform. This kind of dynamic programming is typically called nonserial polyadic dynamic programming. Owing to the: non-uniform data dependence;it is harder to optimize this problem for parallelism and locality on parallel architectures. In this paper, we address the chanllenge of exploiting fine grain parallelism and locality of nonserial polyadic dynamic programming on a multi-core architecture. We present a programming and execution model for multi-core architectures with memory hierarchy. In the framework of the new model, the parallelism and locality benifit from a data dependence transformation. We propose a parallel pipelined algorithm for filling the dynamic programming matrix by decomposing the computation operators. The new parallel algorithm tolerates the memory access latency using multi-thread and is easily improved with the technique. We formulate and analytically solve the optimization problem determing the the size that minimizes the total execution time. The experiments on a simulator give a validation of the proposed model and show that the fine grain parallel algorithm achieves sub-linear speedup and that a potential high scalability on multi-core arichitecture.

关键词： Dynamic Programming Data Dependence Multicore Memory Hierarchy Scalabilitiy

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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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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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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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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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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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Brief Announcement: Serial-parallel Reciprocity in Dynamic Multithreaded Languages 10

Brief Announcement: Serial-Parallel Reciprocity in Dynamic M...

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22nd acm symposium on parallelism in algorithms and architectures

作者： Agrawal, Kunal Lee, I-Ting Angelina Sukha, Jim Washington Univ St Louis MO 63130 USA

ISBN: (纸本)9781450300797

In dynamically multithreaded platforms that employ work stealing, there appears to be a fundamental tradeoff between providing provably good time and space bounds and supporting SP-reciprocity, the property of allowing arbitrary calling between parallel and serial code, including legacy serial binaries. Many known dynamically multithreaded platforms either fail to support SP-reciprocity or sacrifice on the provable time and space bounds that an efficient work-stealing scheduler could otherwise guarantee We describe PR-Cilk, a design of a runtime system that supports SP-reciprocity in Cilk and provides provable bounds on time and space In order to maintain the space bound, PR-Cilk uses subtree-restricted work stealing. We show that with subtree-restricted work stealing. PR-Cilk provides the same guarantee on stack space usage as ordinary Cilk. The completion time guaranteed by PR-Cilk is slightly worse than ordinary Cilk Nevertheless, if the number of times a C function calls a Cilk function is small, or if each Cilk function called by a C function is sufficiently parallel. PR-Cilk still guarantees linear speedup.

关键词： Cilk dynamic multithreading Intel Threading Building Blocks scheduling work stealing serial-parallel reciprocity

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