17105049
Data-Driven Time-Parallelization in the AFM Simulation of Proteins
Molecular dynamics is a popular technique to simulate the behavior of physical systems, with resolution at the atomic scale. One of its limitations is that an enormous computational effort is required to simulate to realistic time spans. Conventional parallelization strategies have limited effectiveness in dealing with this difficulty. We recently introduced a more scalable approach to parallelization, where data from prior, related, simulations are used to parallelize a simulation in the time domain. We demonstrated its effectiveness in nano-mechanics simulations. In this paper, we develop our approach so that it can be used in a soft-matter application involving the atomic force microscopy simulation of proteins. We obtain an order of magnitude improvement in performance when we combine time parallelization with conventional parallelization. The significance of this work lies in demonstrating the promise of data-driven time parallelization in soft-matter applications, which are more challenging than the hard-matter applications considered earlier.
37521671
Latency tolerance through parallelization of time in scientific applications
Emerging computing environments, such as the Grid, promise enormous raw computational power. However, effective use of such platforms is often difficult, because conventional spatial decomposition leads to fine granularity, resulting in high communication overhead. We introduce the concept of guided simulations to parallelize along the time domain. Here, we use the fact that typically results of other simulations of closely related problems are available. In this approach, we automatically and dynamically determine a relationship between old simulations and the one being performed, and use this to parallelize along the time domain. We demonstrate the validity of this approach by applying the technique to an important application involving molecular dynamics simulation of nanomaterials. In this application, spatial decomposition is not effective due to the small size of the physical system. However, time parallelization is effective, since the granularity is much coarser. We also mention how this approach can be extended to make it inherently fault tolerant.
28892549
Improved Monte Carlo Linear Solvers Through Non-diagonal Splitting
Fast, but approximate, solutions to linear algebra problems have many potential applications, such as in graph partitioning, preconditioning, information retrieval, etc. Monte Carlo techniques appear attractive for such needs. While Monte Carlo linear solvers have a long history, their application has been limited due to slow convergence. Despite the development of techniques to improve their accuracy, current methods suffer from the drawback that they are stochastic realizations of inherently poor iterative methods. The reason for such choices is the need for efficient Monte Carlo implementation, which has restricted the splittings that are considered. However, in this paper we demonstrate that such restrictions are not necessarily required, and that efficient Monte Carlo implementations are possible even with splittings that do not appear amenable to it.
36642411
Parameterizing parallel multiplicative lagged-Fibonacci generators
Monte Carlo computations are commonly considered to be naturally parallel. However, one needs to exercise care in parallelizing the underlying pseudorandom number generator (PRNG) to avoid correlations within, and between, random number streams. PRNGs are normally parallelized using one of the following two paradigms: (i) cycle division and (ii) parameterization. Most of the popular PRNGs based on linear recurrences, such as linear congruential generators (LCGs), generalized feedback shift-register generators (GFSRs), and additive lagged-Fibonacci generators (ALFGs) have been parallelized using both these paradigms. While the (nonlinear) multiplicative lagged-Fibonacci generators (MLFG) is considered superior to the ALFG in quality, it had so far been parallelized only via the cycle division paradigm, which has its limitations. In this paper, we describe parallelization of the MLFG using parameterization, and discuss its implementation in the Scalable Parallel Random Number Generators (SPRNG) [ACM Trans. Math. Software 26 (2000) 436] parallel pseudorandom number generation software. We also present empirical results demonstrating the quality, and quantitatively compare the parallel ALFGs and MLFGs quality.
15947258
Domain Decomposition for Particle Methods on the Sphere
We present an algorithm for efficient parallelization of particle methods when the domain is the surface of a sphere. Such applications typically arise when dealing with directional data. We propose a domain decomposition scheme based on geometric partitioning that provides domains suitable for practical implementation. This algorithm has the advantage of being fast enough to be applied dynamically, and at the same time provides good partitions, comparable in quality to those produced by spectral graph partitioning schemes.
16971481
Image compression for fast wavelet-based subregion retrieval
In an image browsing environment there is need for progressively viewing image subregions at various resolutions. We describe a storage scheme that accomplishes good image compression, while supporting fast image subregion retrieval. We evaluate analytically and experimentally the compression performance of our algorithm. We also provide results on the speed of the algorithm to demonstrate its effectiveness, and present an extension to a client/server environment.
18673248
Mixed Pfair/ERfair scheduling of asynchronous periodic tasks
Pfair scheduling was proposed by Baruah, Cohen, Plaxton, and Varvel as a non-work-conserving way of optimally and efficiently scheduling periodic tasks on a multiprocessor. In this paper, we introduce a work-conserving variant of Pfair scheduling called "early-release" fair (ERfair) scheduling. We also present a new scheduling algorithm called PD2 and show that it is optimal for scheduling any mix of early-release and non-early-release asynchronous, periodic tasks. In contrast, almost all prior work on Pfair scheduling has been limited to synchronous systems. PD2 is an optimization of an earlier deadline-based algorithm of Baruah, Gehrke, and Plaxton called PD; PD2 uses a simpler tie-breaking scheme than PD to dis ambiguate equal deadlines. We present a series of counterexamples that suggest that, in general, the PD2 tie-breaking mechanism cannot be simplified. In contrast to this, we show that no tie-breaking information is needed on two-processor systems.
2418753
Computing with very weak random sources
For any fixed /spl epsiv/>0, we show how to simulate RP algorithms in time n/sup O(log n/) using the output of a /spl delta/-source with min-entropy R(/spl epsiv/). Such a weak random source is asked once for R(/spl epsiv/) bits; it outputs an R-bit string such that any string has probability at most 2/sup -R/(/spl epsiv//). If /spl epsiv/>1-1/(k+1), our BPP simulations take time n/sup O(log(k/ n)) (log/sup (k/) is the logarithm iterated k times). We also give a polynomial-time BPP simulation using Chor-Goldreich sources of min-entropy R/sup /spl Omega/(1/), which is optimal. We present applications to time-space tradeoffs, expander constructions, and the hardness of approximation. Also of interest is our randomness-efficient Leftover Hash Lemma, found independently by Goldreich and Wigderson.<<ETX>>
18206354
Optimal design of signaling networks for Internet telephony
We present an approach for efficient design of a signaling network for a network of software switches supporting Internet telephony. While one may take an integer programming approach to solve this problem, it quickly becomes intractable even for modest-sized networks. Instead, our topology design uses random graphs that we show to be nearly optimal in cost, highly connected, and computationally efficient even for large networks. We then formulate a quadratic assignment problem (QAP) to map the abstract topology into the physical network to achieve optimal load balancing for given demand forecasts, which we solve using randomized heuristics. Numerical results on several example networks illustrate the performance and computational efficiency of our method. A graphical design tool has been developed based on our algorithms.
47213893
A Constant-Factor Approximation Algorithm for Packet Routing and Balancing Local vs. Global Criteria
We present the first constant-factor approximation algorithm for a fundamental problem: the store-and-forward packet routing problem on arbitrary networks. Furthermore, the queue sizes required at the edges are bounded by an absolute constant. Thus, this algorithm balances a global criterion (routing time) with a local criterion (maximum queue size) and shows how to get simultaneous good bounds for both. For this particular problem, approximating the routing time well, even without considering the queue sizes, was open. We then consider a class of such local vs. global problems in the context of covering integer programs and show how to improve the local criterion by a logarithmic factor by losing a constant factor in the global criterion.
37206769
Finding Large Independent Sets in Graphs and Hypergraphs
A basic problem in graphs and hypergraphs is that of finding a large independent set---one of guaranteed size. Understanding the parallel complexity of this and related independent set problems on hypergraphs is a fundamental open issue in parallel computation. Caro and Tuza [J. Graph Theory, 15 (1991), pp. 99--107] have shown a certain lower bound $\alpha_k(H)$ on the size of a maximum independent set in a given k-uniform hypergraph H and have also presented an efficient sequential algorithm to find an independent set of size $\alpha_k(H)$. They also show that $\alpha_k(H)$ is the size of the maximum independent set for various hypergraph families. Here, we show that an RNC algorithm due to Beame and Luby [in Proceedings of the ACM--SIAM Symposium on Discrete Algorithms, 1990, pp. 212--218] finds an independent set of expected size $\alpha_k(H)$ and also derandomizes it for certain special cases. (An intriguing conjecture of Beame and Luby implies that understanding this algorithm better may yield an RNC...