6068249
Dynamic Load Balancing for Finite Element Calculations on Parallel Computers
Computational requirements of full scale computational fluid dynamics change as computation progresses on a parallel machine. The change in computational intensity causes workload imbalance of processors, which in turn requires a large amount of data movement at runtime. If parallel CFD is to be successful on a parallel or massively parallel machine, balancing of the runtime load is indispensable. Here a frame work is presented for dynamic load balancing for CFD applications, called Jove. One processor is designated as a decision maker Jove while others are assigned to computational fluid dynamics. P l ocessors running CFD send flags to Jove in a predetermined number of iterations to nitiate load balancing. Jove starts working on load balancing while other processors c ntinue working with the current data and load distribution. Jove goes through several steps to decide if the new data should be taken, including preliminary evaluate, partition, processor reassignment, cost evaluation, and decision. Jove running on a single SP2 node has been completely implemented. Preliminary experimental results show that the Jove approach to dynamic load balancing can be effective for full scale grid partitioning on the target machine SP2.
38908855
Large-Scale SVD and Subspace-Based Methods for Information Retrieval
A theoretical foundation for latent semantic indexing (LSI) is proposed by adapting a model first used in array signal processing to the context of information retrieval using the concept of subspaces. It is shown that this subspace-based model coupled with minimal description length (MDL) principle leads to a statistical test to determine the dimensions of the latent-concept subspaces in LSI. The effect of weighting on the choice of the optimal dimensions of latent-concept subspaces is illustrated. It is also shown that the model imposes a so-called low-rank-plus-shift structure that is approximately satisfied by the cross-product of the term-document matrices. This structure can be exploited to give a more accurate updating scheme for LSI and to correct some of the misconception about the achievable retrieval accuracy in LSI updating. Variants of Lanczos algorithms are illustrated with numerical test results on Cray T3E using document collections generated from World Wide Web.
46294089
1992 Gordon Bell Prize Winners
35264400
Parallel Efficiency of the Lanczos Method for Eigenvalue Problems
LBNL-42828 Parallel Efficiency of the Lanczos Method for Eigenvalue Problems ^ Kesheng Wu+and Horst Simon* Abstract Two of the commonly used versions of the Lanczos method for eigenvalues problems are the shift-and-invert Lanczos method and the restarted Lanczos method. In this talk, we will address two questions, is the shift-and-invert Lanczos method a viable option on massively parallel machines and which one is more appropriate for a given eigenvalue problem? Introduction T h i s talk is o n how to compute eigenvalues a n d eigenvectors of large sparse s y m m e t r i c matrices o n massively parallel machines. One of the the most c o m m o n l y used algorithms for this task is the Lanczos m e t h o d w h i c h projects the large eigenvalue p r o b l e m onto a low dimensional K r y l o v subspace [7, 10]. I n most cases, the K r y l o v subspace basis is built t h r o u g h a series of matrix-vector m u l t i p l i c a t i o n s , the whole Lanczos m e t h o d c a n be implemented w i t h a matrix-vector m u l t i p l i c a t i o n routine a n d a few simple vector operations. T h i s a l g o r i t h m is highly efficient on parallel machines a n d it is effective for c o m p u t i n g extreme a n d well separated eigenvalues. To compute the interior or not well-separated eigenvalues, the shift-and-invert Lanczos m e t h o d is one of the most effective methods. Since the eigenvalues of a m a t r i x A are related to the eigenvalues of (A — c r l ) by a simple relation X(A) = a + 1/X((A — c r l ) ) a n d the corresponding eigenvectors of A a n d (A — c r l ) are identical, the shift-and-invert scheme computes the extreme eigenvalues of (A — c r l ) a n d deduce the corresponding eigenvalues of A. W i t h appropriate choice of a, the extreme eigenvalues of (A — al)^ are well separated and can be easily computed. T h e shift-and-invert Lanczos m e t h o d needs to b u i l d a K r y l o v subspace basis of (A — c r l ) w h i c h is done by solving a series of linear systems involving the coefficient m a t r i x (A — a I). T h e linear systems need to be solved accurately a n d the only reliable means to accomplish this is by using a direct m e t h o d [5]. Because it is difficult to implement direct methods o n d i s t r i b u t e d parallel computers, efficient parallel i m p l e m e n t a t i o n has not been widely available u n t i l recently [1, 8]. T h i s talk w i l l present our s t u d y of the parallel efficiency of the shift-and-invert Lanczos m e t h o d using these newly available direct solvers. T h e study w i l l show that the shift-and-invert Lanczos m e t h o d is ' T h i s w o r k was s u p p o r t e d b y t h e D i r e c t o r , Office o f E n e r g y R e s e a r c h , Office o f L a b o r a t o r y P o l i c y a n d Infrastructure M a n a g e m e n t , of the U . S . D e p a r t m e n t of E n e r g y under C o n t r a c t N o . D E - A C 0 3 - 7 6 S F 0 0 0 9 8 . T h i s r e s e a r c h u s e d r e s o u r c e s o f t h e N a t i o n a l E n e r g y R e s e a r c h S c i e n t i f i c C o m p u t i n g C e n t e r , w h i c h is s u p p o r t e d b y t h e Office o f E n e r g y R e s e a r c h o f t h e U . S . D e p a r t m e n t o f E n e r g y . 'Lawrence Berkeley National Laboratory/NERSC, Berkeley, CA Email: {ksni, hdsimon}81bl.gov.
36271721
Industrial Application Areas of High-Performance Computing
In 1993, a list of the top 500 supercomputer sites worldwide was made available for the first time. Since then, the Top500 list has been published twice a year. The list allows a detailed and well-founded analysis of the state of high-performance computing (HPC). This article summarizes the recent trends in application areas of HPC systems, focusing on the increase in industrial installations and applications.
9150119
Thick-Restart Lanczos Method for Symmetric Eigenvalue Problems
This paper describes a restarted Lanczos algorithm that particularly suitable for implementation on distributed machines. The only communication operation is requires outside of the matrix-vector multiplication is a global sum. For most large eigenvalue problems, the global sum operation takes a small fraction of the total execution time. The majority of the computer is spent in the matrix-vector multiplication. Efficient parallel matrix-vector multiplication routines can be found in many parallel sparse matrix packages such as AZTEC [9], BLOCK-SOLVE [10], PETSc [3], P_SPARSLIB. For this reason, our main emphasis in this paper is to demonstrate the correctness and the effectiveness of the new algorithm.
14801431
Causality in Bayesian Belief Networks
We address the problem of causal interpretation of the graphical structure of Bayesian belief networks (BBNs). We review the concept of causality explicated in the domain of structural equations models and show that it is applicable to BBNs. In this view, which we call mechanism-based, causality is defined within models and causal asymmetries arise when mechanisms are placed in the context of a system. We lay the link between structural equations models and BBNs models and formulate the conditions under which the latter can be given causal interpretation.
1182152
Stability of k -Means Clustering
We consider the stability of k-means clustering problems. Clustering stability is a common heuristics used to determine the number of clusters in a wide variety of clustering applications. We continue the theoretical analysis of clustering stability by establishing a complete characterization of clustering stability in terms of the number of optimal solutions to the clustering optimization problem. Our results complement earlier work of Ben-David, von Luxburg and Pal, by settling the main problem left open there. Our analysis shows that, for probability distributions with finite support, the stability of k-means clusterings depends solely on the number of optimal solutions to the underlying optimization problem for the data distribution. These results challenge the common belief and practice that view stability as an indicator of the validity, or meaningfulness, of the choice of a clustering algorithm and number of clusters.
17442679
Inner Product Spaces for Bayesian Networks
Bayesian networks have become one of the major models used for statistical inference. We study the question whether the decisions computed by a Bayesian network can be represented within a low-dimensional inner product space. We focus on two-label classification tasks over the Boolean domain. As main results we establish upper and lower bounds on the dimension of the inner product space for Bayesian networks with an explicitly given (full or reduced) parameter collection. In particular, these bounds are tight up to a factor of 2. For some nontrivial cases of Bayesian networks we even determine the exact values of this dimension. We further consider logistic autoregressive Bayesian networks and show that every sufficiently expressive inner product space must have dimension at least Ω(n2), where n is the number of network nodes. We also derive the bound 2Ω(n) for an artificial variant of this network, thereby demonstrating the limits of our approach and raising an interesting open question. As a major technical contribution, this work reveals combinatorial and algebraic structures within Bayesian networks such that known methods for the derivation of lower bounds on the dimension of inner product spaces can be brought into play.
37804897
Directions for Qualitative Reasoning
Sacks & Doyle provide an excellent overview of the fundamental limitations of the SPQR representations for reasoning about the qualitative properties of dynamic systems. We take this opportunity to outline some new directions for qualitative reasoning. In this paper, we provide a rigorous mathematical characterization for the term “qualitative property” in the context of static and dynamic systems. Based on these characterizations, we show that interval representations are well suited for reasoning about the qualitative properties of static systems such as qualitative comparative statics and qualitative stability. Moreover, we also show that symbolic computations help in the derivation of useful global properties of dynamic systems which can be used to guide numerical sampling of differential equations. The integration of symbolic and numeric methods provides a powerful approach for automating the qualitative analysis of differential equations.
42465992
History of Artificial Intelligence
Though our discussion is e n t i t l e d "The History o f A r t i f i c i a l I n te l l i gence" , i n fac t we are focusing here on one b r i e f but h igh ly s i gn i f i can t moment in that h i s t o r y , the moment when a r t metamorphosed i t s e l f i n to science, from wish and dream to something l i k e r e a l i t y . As you w i l l learn from each of the discussants, th is metamorphosis took place at several locat ions during the ear ly to mid-1950s, and i t s ca ta lys t was the recogni t ion that the computer was the most promising medium yet in which to rea l i ze what had been a human dream since ea r l i es t t imes, the creat ion of man-made, rather than begotten i n te l l i gence .