Parallel and vector computation for stochastic optimal control applications

A general method for parallel and vector numerical solutions of stochastic dynamic programming problems is described for optimal control of general nonlinear, continuous time, multibody dynamical systems, perturbed by Poisson as well as Gaussian random white noise. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random atmospheric fluctuations. The numerical formulation is highly suitable for a vector multiprocessor or vectorizing supercomputer, and results exhibit high processor efficiency and numerical stability. Advanced computing techniques, data structures, and hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations

\u3cem\u3ek-k\u3c/em\u3e Routing, \u3cem\u3ek-k\u3c/em\u3e Sorting, and Cut Through Routing on the Mesh

In this paper we present randomized algorithms for k-k routing, k-k sorting, and cut through routing. The stated resource bounds hold with high probability. The algorithm for k-k routing runs in [k/2]n+o(kn) steps. We also show that k-k sorting can be accomplished within [k/2] n+n+o(kn) steps, and cut through routing can be done in [3/4]kn+[3/2]n+o(kn) steps. The best known time bounds (prior to this paper) for all these three problems were kn+o(kn). [kn/2] is a known lower bound for all the three problems (which is the bisection bound), and hence our algorithms are very nearly optimal. All the above mentioned algorithms have optimal queue length, namely k+o(k). These algorithms also extend to higher dimensional meshes

Sample sort on meshes

This paper provides an overview of lower and upper bounds for mesh-connected processor networks. Most attention goes to routing and sorting problems, but other problems are mentioned as well. Results from 1977 to 1995 are covered. We provide numerous results, references and open problems. The text is completed with an index. This is a worked-out version of the author's contribution to a joint paper with Grammatikakis, Hsu and Kraetzl on multicomputer routing, submitted to JPDC

Randomized Routing and Sorting on the Reconfigurable Mesh

In this paper we demonstrate the power of reconfiguration by presenting efficient randomized algorithms for both packet routing and sorting on a reconfigurable mesh connected computer (referred to simply as the mesh from hereon). The run times of these algorithms are better than the best achievable time bounds on a conventional mesh. In particular, we show that permutation routing problem can be solved on a linear array of size n in 3/4n steps, whereas n-1 is the best possible run time without reconfiguration. We also show that permutation routing on an n x n reconfigurable mesh can be done in time n + o(n)using a randomized algorithm or in time 1.25n + o(n) deterministically. In contrast, 2n-2 is the diameter of a conventional mesh and hence routing and sorting will need at least 2n-2 steps on a conventional mesh. In addition we show that the problem of sorting can be solved in time n+ o(n). All these time bounds hold with high probability. The bisection lower bound for both sorting and routing on the mesh is n/2, and hence our algorithms have nearly optimal time bounds

Efficient parallel computation on multiprocessors with optical interconnection networks

This dissertation studies optical interconnection networks, their architecture, address schemes, and computation and communication capabilities. We focus on a simple but powerful optical interconnection network model - the Linear Array with Reconfigurable pipelined Bus System (LARPBS). We extend the LARPBS model to a simplified higher dimensional LAPRBS and provide a set of basic computation operations. We then study the following two groups of parallel computation problems on both one dimensional LARPBS\u27s as well as multi-dimensional LARPBS\u27s: parallel comparison problems, including sorting, merging, and selection; Boolean matrix multiplication, transitive closure and their applications to connected component problems. We implement an optimal sorting algorithm on an n-processor LARPBS. With this optimal sorting algorithm at disposal, we study the sorting problem for higher dimensional LARPBS\u27s and obtain the following results: • An optimal basic Columnsort algorithm on a 2D LARPBS. • Two optimal two-way merge sort algorithms on a 2D LARPBS. • An optimal multi-way merge sorting algorithm on a 2D LARPBS. • An optimal generalized column sort algorithm on a 2D LARPBS. • An optimal generalized column sort algorithm on a 3D LARPBS. • An optimal 5-phase sorting algorithm on a 3D LARPBS. Results for selection problems are as follows: • A constant time maximum-finding algorithm on an LARPBS. • An optimal maximum-finding algorithm on an LARPBS. • An O((log log n)2) time parallel selection algorithm on an LARPBS. • An O(k(log log n)2) time parallel multi-selection algorithm on an LARPBS. While studying the computation and communication properties of the LARPBS model, we find Boolean matrix multiplication and its applications to the graph are another set of problem that can be solved efficiently on the LARPBS. Following is a list of results we have obtained in this area. • A constant time Boolean matrix multiplication algorithm. • An O(log n)-time transitive closure algorithm. • An O(log n)-time connected components algorithm. • An O(log n)-time strongly connected components algorithm. The results provided in this dissertation show the strong computation and communication power of optical interconnection networks

Randomized Algorithms For Packet Routing on the Mesh

Packet routing is an important problem of parallel computing since a fast algorithm for packet routing will imply 1) fast inter-processor communication, and 2) fast algorithms for emulating ideal models like PRAMs on fixed connection machines.There are three different models of packet routing, namely 1) Store and forward, 2) Multipacket, and 3) Cut through. In this paper we provide a survey of the best known randomized algorithms for store and forward routing, k-k routing, and cut through routing on the Mesh Connected Computers

Mesh Connected Computers With Multiple Fixed Buses: Packet Routing, Sorting and Selection

Mesh connected computers have become attractive models of computing because of their varied special features. In this paper we consider two variations of the mesh model: 1) a mesh with fixed buses, and 2) a mesh with reconfigurable buses. Both these models have been the subject matter of extensive previous research. We solve numerous important problems related to packet routing, sorting, and selection on these models. In particular, we provide lower bounds and very nearly matching upper bounds for the following problems on both these models: 1) Routing on a linear array; and 2) k-k routing, k-k sorting, and cut through routing on a 2D mesh for any k ≥ 12. We provide an improved algorithm for 1-1 routing and a matching sorting algorithm. In addition we present greedy algorithms for 1-1 routing, k-k routing, cut through routing, and k-k sorting that are better on average and supply matching lower bounds. We also show that sorting can be performed in logarithmic time on a mesh with fixed buses. As a consequence we present an optimal randomized selection algorithm. In addition we provide a selection algorithm for the mesh with reconfigurable buses whose time bound is significantly better than the existing ones. Our algorithms have considerably better time bounds than many existing best known algorithms

Space-Efficient Parallel Algorithms for Combinatorial Search Problems

We present space-efficient parallel strategies for two fundamental combinatorial search problems, namely, backtrack search and branch-and-bound, both involving the visit of an $n$-node tree of height $h$ under the assumption that a node can be accessed only through its father or its children. For both problems we propose efficient algorithms that run on a $p$-processor distributed-memory machine. For backtrack search, we give a deterministic algorithm running in $O(n/p+h\log p)$ time, and a Las Vegas algorithm requiring optimal $O(n/p+h)$ time, with high probability. Building on the backtrack search algorithm, we also derive a Las Vegas algorithm for branch-and-bound which runs in $O((n/p+h\log p \log n)h\log^2 n)$ time, with high probability. A remarkable feature of our algorithms is the use of only constant space per processor, which constitutes a significant improvement upon previous algorithms whose space requirements per processor depend on the (possibly huge) tree to be explored.Comment: Extended version of the paper in the Proc. of 38th International Symposium on Mathematical Foundations of Computer Science (MFCS

Simulation Of Multi-core Systems And Interconnections And Evaluation Of Fat-Mesh Networks

Simulators are very important in computer architecture research as they enable the exploration of new architectures to obtain detailed performance evaluation without building costly physical hardware. Simulation is even more critical to study future many-core architectures as it provides the opportunity to assess currently non-existing computer systems. In this thesis, a multiprocessor simulator is presented based on a cycle accurate architecture simulator called SESC. The shared L2 cache system is extended into a distributed shared cache (DSC) with a directory-based cache coherency protocol. A mesh network module is extended and integrated into SESC to replace the bus for scalable inter-processor communication. While these efforts complete an extended multiprocessor simulation infrastructure, two interconnection enhancements are proposed and evaluated. A novel non-uniform fat-mesh network structure similar to the idea of fat-tree is proposed. This non-uniform mesh network takes advantage of the average traffic pattern, typically all-to-all in DSC, to dedicate additional links for connections with heavy traffic (e.g., near the center) and fewer links for lighter traffic (e.g., near the periphery). Two fat-mesh schemes are implemented based on different routing algorithms. Analytical fat-mesh models are constructed by presenting the expressions for the traffic requirements of personalized all-to-all traffic. Performance improvements over the uniform mesh are demonstrated in the results from the simulator. A hybrid network consisting of one packet switching plane and multiple circuit switching planes is constructed as the second enhancement. The circuit switching planes provide fast paths between neighbors with heavy communication traffic. A compiler technique that abstracts the symbolic expressions of benchmarks' communication patterns can be used to help facilitate the circuit establishment

A scalable multi-core architecture with heterogeneous memory structures for Dynamic Neuromorphic Asynchronous Processors (DYNAPs)

Neuromorphic computing systems comprise networks of neurons that use asynchronous events for both computation and communication. This type of representation offers several advantages in terms of bandwidth and power consumption in neuromorphic electronic systems. However, managing the traffic of asynchronous events in large scale systems is a daunting task, both in terms of circuit complexity and memory requirements. Here we present a novel routing methodology that employs both hierarchical and mesh routing strategies and combines heterogeneous memory structures for minimizing both memory requirements and latency, while maximizing programming flexibility to support a wide range of event-based neural network architectures, through parameter configuration. We validated the proposed scheme in a prototype multi-core neuromorphic processor chip that employs hybrid analog/digital circuits for emulating synapse and neuron dynamics together with asynchronous digital circuits for managing the address-event traffic. We present a theoretical analysis of the proposed connectivity scheme, describe the methods and circuits used to implement such scheme, and characterize the prototype chip. Finally, we demonstrate the use of the neuromorphic processor with a convolutional neural network for the real-time classification of visual symbols being flashed to a dynamic vision sensor (DVS) at high speed.Comment: 17 pages, 14 figure