Simulating a Pipelined Reconfigurable Mesh on a Linear Array with a Reconfigurable Pipelined Bus System

Due to the unidirectional nature of propagation and predictable delays, optically pipelined buses have been gaining more attention. There have been many models proposed over time that use reconfigurable optically pipelined buses. The reconfigurable nature of the models makes them capable of changing their component’s functionalities and structure that connects the components at every step of computation. There are both one dimensional as well as k –dimensional models that have been proposed in the literature. Though equivalence between various one dimensional models and equivalence between different two dimensional models had been established, so far there has not been any attempt to explore the relationship between a one dimensional model and a two dimensional model. In the proposed research work it is shown that a move from one to two or more dimensions does not cause any increase in the volume of communication between the processors as they communicate in a pipelined manner on the same optical bus. When moving from two dimensions to one dimension, the challenge is to map the processors so that those belonging to a two-dimensional bus segment are contiguous and in the same order on the one-dimensional model. This does not increase any increase in communication overhead as the processors instead of communicating on two dimensional buses now communicate on a linear one dimensional bus structure. To explore the relationship between one dimensional and two dimensional models a commonly used model Linear Array with a Reconfigurable Pipelined Bus System (LARPBS) and its two dimensional counterpart Pipelined Reconfigurable Mesh (PR-Mesh) are chosen Here an attempt has been made to present a simulation of a two dimensional PR-Mesh on a one dimensional LARPBS to establish complexity of the models with respect to one another, and to determine the efficiency with which the LARPBS can simulate the PR-Mesh

Parallel progressive multiple sequence alignment on reconfigurable meshes

<p>Abstract</p> <p>Background</p> <p>One of the most fundamental and challenging tasks in bio-informatics is to identify related sequences and their hidden biological significance. The most popular and proven best practice method to accomplish this task is aligning multiple sequences together. However, multiple sequence alignment is a computing extensive task. In addition, the advancement in DNA/RNA and Protein sequencing techniques has created a vast amount of sequences to be analyzed that exceeding the capability of traditional computing models. Therefore, an effective parallel multiple sequence alignment model capable of resolving these issues is in a great demand.</p> <p>Results</p> <p>We design <it>O</it>(1) run-time solutions for both local and global dynamic programming pair-wise alignment algorithms on reconfigurable mesh computing model. To align <it>m </it>sequences with max length <it>n</it>, we combining the parallel pair-wise dynamic programming solutions with newly designed parallel components. We successfully reduce the progressive multiple sequence alignment algorithm's run-time complexity from <it>O</it>(<it>m </it>× <it>n</it>⁴) to <it>O</it>(<it>m</it>) using <it>O</it>(<it>m </it>× <it>n</it>³) processing units for scoring schemes that use three distinct values for match/mismatch/gap-extension. The general solution to multiple sequence alignment algorithm takes <it>O</it>(<it>m </it>× <it>n</it>⁴) processing units and completes in <it>O</it>(<it>m</it>) time.</p> <p>Conclusions</p> <p>To our knowledge, this is the first time the progressive multiple sequence alignment algorithm is completely parallelized with <it>O</it>(<it>m</it>) run-time. We also provide a new parallel algorithm for the Longest Common Subsequence (LCS) with <it>O</it>(1) run-time using <it>O</it>(<it>n</it>³) processing units. This is a big improvement over the current best constant-time algorithm that uses <it>O</it>(<it>n</it>⁴) processing units.</p

Simulations and Algorithms on Reconfigurable Meshes With Pipelined Optical Buses.

Recently, many models using reconfigurable optically pipelined buses have been proposed in the literature. A system with an optically pipelined bus uses optical waveguides, with unidirectional propagation and predictable delays, instead of electrical buses to transfer information among processors. These two properties enable synchronized concurrent access to an optical bus in a pipelined fashion. Combined with the abilities of the bus structure to broadcast and multicast, this architecture suits many communication-intensive applications. We establish the equivalence of three such one-dimensional optical models, namely the LARPBS, LPB, and POB. This implies an automatic translation of algorithms (without loss of speed or efficiency) among these models. In particular, since the LPB is the same as an LARPBS without the ability to segment its buses, their equivalence establishes reconfigurable delays (rather than segmenting ability) as the key to the power of optically pipelined models. We also present simulations for a number of two-dimensional optical models and establish that they possess the same complexity, so that any of these models can simulate a step of one of the other models in constant time with a polynomial increase in size. Specifically, we determine the complexity of three two-dimensional optical models (the PR-Mesh, APPBS, and AROB) to be the same as the well known LR-Mesh and the cycle-free LR-Mesh. We develop algorithms for the LARPBS and PR-Mesh that are more efficient than existing algorithms in part by exploiting the pipelining, segmenting, and multicasting characteristics of these models. We also consider the implications of certain physical constraints placed on the system by restricting the distance over which two processors are able to communicate. All algorithms developed for these models assume that a healthy system is available. We present some fundamental algorithms that are able to tolerate up to N/2 faults on an N-processor LARPBS. We then extend these results to apply to other algorithms in the areas of image processing and matrix operations

Scaling Simulations of Reconfigurable Meshes.

This dissertation deals with reconfigurable bus-based models, a new type of parallel machine that uses dynamically alterable connections between processors to allow efficient communication and to perform fast computations. We focus this work on the Reconfigurable Mesh (R-Mesh), one of the most widely studied reconfigurable models. We study the ability of the R-Mesh to adapt an algorithm instance of an arbitrary size to run on a given smaller model size without significant loss of efficiency. A scaling simulation achieves this adaptation, and the simulation overhead expresses the efficiency of the simulation. We construct a scaling simulation for the Fusing-Restricted Reconfigurable Mesh (FR-Mesh), an important restriction of the R-Mesh. The overhead of this simulation depends only on the simulating machine size and not on the simulated machine size. The results of this scaling simulation extend to a variety of concurrent write rules and also translate to an improved scaling simulation of the R-Mesh itself. We present a bus linearization procedure that transforms an arbitrary non-linear bus configuration of an R-Mesh into an equivalent acyclic linear bus configuration implementable on an Linear Reconfigurable Mesh (LR-Mesh), a weaker version of the R-Mesh. This procedure gives the algorithm designer the liberty of using buses of arbitrary shape, while automatically translating the algorithm to run on a simpler platform. We illustrate our bus linearization method through two important applications. The first leads to a faster scaling simulation of the R-Mesh. The second application adapts algorithms designed for R-Meshes to run on models with pipelined optical buses. We also present a simulation of a Directional Reconfigurable Mesh (DR-Mesh) on an LR-Mesh. This simulation has a much better efficiency compared to previous work. In addition to the LR-Mesh, this simulation also runs on models that use pipelined optical buses

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