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Deterministic algorithms for the Lov′asz Local Lemma: simpler, more general, and more parallel 33

Deterministic algorithms for the Lov′asz Local Lemma: simpl...

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annual acm-SIAM symposium on Discrete algorithms (SODA)

作者： Harris, David G. Univ Maryland Dept Comp Sci College Pk MD 20742 USA

ISBN: (纸本)9781611977073

The Lov ' asz Local Lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid a collection B of "bad" events which are mostly independent and have low probability. In its simplest "symmetric" form, it asserts that whenever a bad-event has probability p and affects at most d bad-events, and epd < 1, then a configuration avoiding all B exists. A seminal algorithm of Moser & Tardos (2010) (which we call the MT algorithm) gives nearly-automatic randomized algorithms for most constructions based on the LLL. However, deterministic algorithms have lagged behind. We address three specific shortcomings of the prior deterministic algorithms. First, our algorithm applies to the LLL criterion of Shearer (1985);this is more powerful than alternate LLL criteria and also removes a number of nuisance parameters and leads to cleaner and more legible bounds. Second, we provide parallel algorithms with much greater flexibility in the functional form of the bad-events. Third, we provide a derandomized version of the MT-distribution, that is, the distribution of the variables at the termination of the MT algorithm. We show applications to non-repetitive vertex coloring, independent transversals, strong coloring, and other problems. These give deterministic algorithms which essentially match the best previous randomized sequential and parallel algorithms.

关键词： parallel algorithms

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Much Ado about Two (Pearl) A Pearl on parallel Prefix Computation

Much Ado about Two (<i>Pearl</i>) A Pearl on Parallel Prefix...

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35th acm-SIGPLAN-SIGACT symposium on Principles of Programming Languages

作者： Voigtlaender, Janis Tech Univ Dresden Inst Theoret Informat D-01062 Dresden Germany

This pearl develops a statement about parallel Prefix Computation in the spirit of Knuth's 0-1-Principle for oblivious sorting algorithms. It turns out that 0-1 is not quite enough here. The perfect hammer for the... 详细信息

ISBN: (纸本)9781595936899

关键词： 0-1-principle free theorems parallel prefix computation relational parametricity

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Efficient computations on fault-prone BSP machines 97

Efficient computations on fault-prone BSP machines

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Proceedings of the 1997 9th annual acm symposium on parallel algorithms and architectures, SPAA

作者： Kontogiannis, Spyros C. Pantzio, Grammati E. Spirakis, Paul G. Patras Univ Patras Greece

ISBN: (纸本)9780897918909

In this paper general simulations of algorithms designed for fully operational BSP machines on BSP machines with faulty or unavailable processors, are developed. The fail-stop model is considered for the fault occurrences, that is, if a processor fails or becomes unavailable, it remains so until the end of the computation. The faults are random, in the sense that a processor may fail independently with probability at most a, where a is a constant. Two possible settings for fault occurrences are considered: the static case where the faults are static (the faulty or unavailable processors are already known at the beginning of the computation), and the dynamic case where the processors may become faulty or unavailable during the computation. In the case of static faults, a simulation of an n-processor fault-free BSP machine on a faulty n-processor BSP machine is presented with constant slowdown per local computation step and O(log n·max{L, g}) slowdown per communication step, given that a preprocessing has been done that needs O(n/log n·max{L, g}) time (L and g are the parameters of the simulating BSP machine). In the case of dynamic faults, a simulation of an n-processor fault-free BSP machine on an cn·log n-processor faulty BSP machine is presented. No dynamic faults may occur during certain periods of the simulation. The simulations are randomized and Monte Carlo: they are guaranteed to be correct with high probability, and the time bounds always hold. To our knowledge, no previous work on the fault tolerance of the BSP model exists.

关键词： parallel processing systems

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Deadlock-free routing in arbitrary networks via the flattest common supersequence method 98

Deadlock-free routing in arbitrary networks via the flattest...

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

作者： Laing, A.K. Cypher, R. The Johns Hopkins Univ Baltimore MD United States

ISBN: (纸本)9780897919890

In this paper we consider the problem of deadlock-free routing in arbitrary parallel and distributed computers. We focus on asynchronous routing algorithms which continuously receive new packets to route and which do not discard packets that encounter congestion. Specifically, we examine what we call the deadlock-free routing (DFR) problem. The input to the DFR problem consists of an arbitrary network and an arbitrary set of paths in the network. The output consists of a routing algorithm, which is a list of the buffers used along each of the paths. The routing algorithm is required to be free from deadlock and the goal is to minimize the number of buffers required in any one node. We study the DFR problem by converting it into an equivalent problem which we call the flattest common supersequence (FCS) problem. The input to the FCS problem consists of a set of sequences and the output consists of a single sequence that contains all of the input sequences as (possibly non-contiguous) subsequences. The goal of the FCS problem is to minimize the maximum frequency of any symbol in the output sequence. We present three main results. First, we prove that the decision version of the FCS problem is NP-complete, and has no polynomial-time approximation scheme unless P = NP. Next, we propose and experimentally evaluate a range of heuristics for FCS. Our experimental results show that one of these heuristics performs very well over a wide range of inputs. Lastly, we prove that this heuristic is in fact optimal for certain restricted classes of inputs.

关键词： parallel algorithms

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Asymptotically tight bounds for performing BMMC permutations on parallel disk systems 93

Asymptotically tight bounds for performing BMMC permutations...

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5th annual acm symposium on parallel algorithms and architectures, SPAA 1993

作者： Cormen, Thomas H. Wisniewski, Leonard F. Department of Mathematics and Computer Science Dartmouth College United States

ISBN: (纸本)0897915992

We give asymptotically equal lower and upper bounds for the number of parallel I/O operations required to perform BMMC permutations (defined by a characteristic matrix that is nonsingular over GF{2)) on parallel disk systems. Under the Vitter-Shriver parallel-disk model with N records, D disks, block size B, and M records of RAM, we show a universal lower bound of Q (l + j)) parallel I/Os for performing a BMMC permutation, where 7 is the lower left lg(N/B) xlgB submatrix of the characteristic matrix. We adapt this lower bound to show that the algorithm for BPC permutations in [Cor93] is asymptotically optimal. We also present an algorithm that uses at most h (6 [is(m/b)1 + 5) parallel I/Os, which asymptotically matches the lower bound and improves upon the BMMC algorithm in [Cor93]. When rank(7) is low, this method is an improvement over the general-permutation bound of Although many BMMC permutations of practical interest fall into subclasses that might be explicitly invoked within the source code, we show how to detect in at most N/BD+ ['SW/H1] parallel I/Os whether a given vector of target addresses specifies a BMMC permutation. Thus, one can determine efficiently at run time whether a permutation to be performed is BMMC and then avoid the general-permutation algorithm and save parallel I/Os by using our algorithm. © 1993 acm.

关键词： Matrix algebra

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Automatic Complexity Analysis of Explicitly parallel Programs 14

Automatic Complexity Analysis of Explicitly Parallel Program...

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26th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Hoefler, Torsten Kwasniewski, Grzegorz Swiss Fed Inst Technol Zurich Switzerland

ISBN: (纸本)9781450328210

The doubling of cores every two years requires programmers to expose maximum parallelism. Applications that are developed on today's machines will often be required to run on many more cores. Thus, it is necessary to understand how much parallelism codes can expose. The work and depth model provides a convenient mental framework to assess the required work and the maximum parallelism of algorithms and their parallel efficiency. We propose an automatic analysis to extract work and depth from a source-code. We do this by statically counting the number of loop iterations depending on the set of input parameters. The resulting expression can be used to assess work and depth with regards to the program inputs. Our method supports the large class of practically relevant loops with affine update functions and generates additional parameters for other expressions. We demonstrate how this method can be used to determine work and depth of several real-world applications. Our technique enables us to prove if the theoretically maximum parallelism is exposed in a practical implementation of a problem. This will be most important for future-proof software development.

关键词： Loop iterations Polyhedral model Work and depth analysis

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SCHEDULING MALLEABLE AND NONMALLEABLE parallel TASKS

SCHEDULING MALLEABLE AND NONMALLEABLE PARALLEL TASKS

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5th annual acm-SIAM symposium on Discrete algorithms

作者： LUDWIG, W TIWARI, P UNIV WISCONSIN DEPT COMP SCIMADISONWI 53706

ISBN: (纸本)0898713293

A malleable parallel task is one that can be executed on any number of processors, with its execution time being a function of the number of processors allotted to it. A nonmalleable parallel task is one that requires a specific number of processors. Given n independent parallel tasks and m identical processors, we consider the problem of scheduling these tasks to minimize makespan. We show that any algorithm for scheduling nonmalleable tasks can be extended to an algorithm for scheduling malleable tasks. The approximation factor of the new algorithm is identical to that of the original algorithm. Meanwhile, only an O(mn) term is added to the running time. Thus we get the best known approximation factor of a polynomial-time algorithm for scheduling malleable parallel tasks, and the fastest running time in which that factor can be achieved. These results can be extended to specific parallel architectures, where not only the number of processors allotted to a task, but also their configuration is a factor. Furthermore, we provide an algorithm for scheduling malleable tasks on a linear array of processors. In this case the addresses of the processors assigned to each task must be contiguous. Our algorithm has an approximation factor of 2, under a natural assumption on the task execution times. In contrast, the best known approximation factor for nonmalleable tasks in this case is 2.5. To the best of our knowledge, this is the only case where the best known approximation factor for malleable tasks is strictly less than that for nonmalleable tasks.

关键词： Storage allocation (computer)

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Collective communication on architectures that support simultaneous communication over multiple links 06

Collective communication on architectures that support simul...

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2006 acm SIGPLAN symposium on Principles and Practice of parallel Programming, PPOPP'06

作者： Chan, Ernie Van De Geijn, Robert Gropp, William Thakur, Rajeev Department of Computer Sciences University of Texas Austin United States Mathematics and Computer Science Division Argonne National Laboratory United States

ISBN: (纸本)1595931899

Traditional collective communication algorithms are designed with the assumption that a node can communicate with only one other node at a time. On new parallel architectures such as the IBM Blue Gene/L, a node can communicate with multiple nodes simultaneously. We have redesigned and reimplemented many of the MPI collective communication algorithms to take advantage of this ability to send simultaneously, including broadcast, reduce(-to-one), scatter, gather, allgather, reduce-scatter, and allreduce. We show that these new algorithms have lower expected costs than the previously known lower bounds based on old models of parallel computation. Results are included comparing their performance to the default implementations in IBM's MPI. Copyright © 2006 acm.

关键词： Telecommunication systems

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A Study of Work Distribution and Contention in Database Primitives on Heterogeneous CPU/GPU architectures 21

A Study of Work Distribution and Contention in Database Prim...

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36th annual acm symposium on Applied Computing (SAC)

作者： Gowanlock, Michael Fink, Zane Karsin, Ben Wright, Jordan No Arizona Univ Sch Informat Comp & Cyber Syst Flagstaff AZ 86011 USA Univ Illinois Dept Comp Sci Urbana IL USA Univ Libre Bruxelles Dept Comp Sci Brussels Belgium

ISBN: (纸本)9781450381048

Graphics Processing Units (GPUs) provide very high on-card memory bandwidth which can be exploited to address data-intensive workloads. To maximize algorithm throughput, it is important to concurrently utilize both the CPU and GPU to carry out database queries. We select data-intensive algorithms that are common in databases and data analytic applications including: (i) scan;(ii) batched predecessor searches;(iii) multiway merging;and, (iv) partitioning. For each algorithm, we examine the performance of parallel CPU/GPU-only, and hybrid CPU/GPU approaches. There are several challenges to combining the CPU and GPU for query processing, including distributing work between architectures. We demonstrate that despite being able to accurately split the work between the CPU and GPU, contention for memory band-width is a major limiting factor for hybrid CPU/GPU data-intensive algorithms. We employ performance models that allowus to explore several research questions. We find that while hybrid data-intensive algorithms may be limited by contention, these algorithms are more robust to workload characteristics;therefore, they are preferable to CPU/GPU-only approaches. We also find that hybrid algorithms achieve good performance when there is low memory contention between the CPU and GPU, such that the GPU can perform its operations without significantly reducing CPU throughput.

关键词： GPGPU Heterogeneous Systems Hybrid algorithms In-memory Database Memory-Bound algorithms Multiway Merge Partitioning Predecessor Search Scan

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On Computing Maximal Independent Sets of Hypergraphs in parallel 14

On Computing Maximal Independent Sets of Hypergraphs in Para...

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26th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Bercea, Ioana O. Goyal, Navin Harris, David G. Srinivasan, Aravind Univ Maryland Dept Comp Sci College Pk MD 20742 USA Microsoft Res India Bangalore Karnataka India Univ Maryland Dept Appl Math College Pk MD 20742 USA Univ Maryland UMIACS College Pk MD 20742 USA

ISBN: (纸本)9781450328210

Whether or not the problem of finding maximal independent sets (MIS) in hypergraphs is in (R)NC is one of the fundamental problems in the theory of parallel computing. Unlike the well-understood case of MIS in graphs, for the hypergraph problem, our knowledge is quite limited despite considerable work. It is known that the problem is in RNC when the edges of the hypergraph have constant size. For general hypergraphs with n vertices and m edges, the fastest previously known algorithm works in time O(root n) with poly(m;n) processors. In this paper we give an EREW PRAM algorithm that works in time n(o(1)) with poly(m;n) processors on general hypergraphs satisfying m <= n log((2))n/ 8(log((3)) n)(2) where log((2)) n = log log n and log((3)) n = log log log n. Our algorithm is based on a sampling idea that reduces the dimension of the hypergraph and employs the algorithm for constant dimension hypergraphs as a subroutine.

关键词： hypergraphs independent sets randomized algorithms parallel algorithms

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