On the design and implementation of broadcast and global combine operations using the postal model

There are a number of models that were proposed in recent years for message passing parallel systems. Examples are the postal model and its generalization the LogP model. In the postal model a parameter λ is used to model the communication latency of the message-passing system. Each node during each round can send a fixed-size message and, simultaneously, receive a message of the same size. Furthermore, a message sent out during round r will incur a latency of hand will arrive at the receiving node at round r + λ - 1. Our goal in this paper is to bridge the gap between the theoretical modeling and the practical implementation. In particular, we investigate a number of practical issues related to the design and implementation of two collective communication operations, namely, the broadcast operation and the global combine operation. Those practical issues include, for example, 1) techniques for measurement of the value of λ on a given machine, 2) creating efficient broadcast algorithms that get the latency hand the number of nodes n as parameters and 3) creating efficient global combine algorithms for parallel machines with λ which is not an integer. We propose solutions that address those practical issues and present results of an experimental study of the new algorithms on the Intel Delta machine. Our main conclusion is that the postal model can help in performance prediction and tuning, for example, a properly tuned broadcast improves the known implementation by more than 20%

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

Multiple Biolgical Sequence Alignment: Scoring Functions, Algorithms, and Evaluations

Aligning multiple biological sequences such as protein sequences or DNA/RNA sequences is a fundamental task in bioinformatics and sequence analysis. These alignments may contain invaluable information that scientists need to predict the sequences\u27 structures, determine the evolutionary relationships between them, or discover drug-like compounds that can bind to the sequences. Unfortunately, multiple sequence alignment (MSA) is NP-Complete. In addition, the lack of a reliable scoring method makes it very hard to align the sequences reliably and to evaluate the alignment outcomes. In this dissertation, we have designed a new scoring method for use in multiple sequence alignment. Our scoring method encapsulates stereo-chemical properties of sequence residues and their substitution probabilities into a tree-structure scoring scheme. This new technique provides a reliable scoring scheme with low computational complexity. In addition to the new scoring scheme, we have designed an overlapping sequence clustering algorithm to use in our new three multiple sequence alignment algorithms. One of our alignment algorithms uses a dynamic weighted guidance tree to perform multiple sequence alignment in progressive fashion. The use of dynamic weighted tree allows errors in the early alignment stages to be corrected in the subsequence stages. Other two algorithms utilize sequence knowledge-bases and sequence consistency to produce biological meaningful sequence alignments. To improve the speed of the multiple sequence alignment, we have developed a parallel algorithm that can be deployed on reconfigurable computer models. Analytically, our parallel algorithm is the fastest progressive multiple sequence alignment algorithm

Scheduling and reconfiguration of interconnection network switches

Interconnection networks are important parts of modern computing systems, facilitating communication between a system\u27s components. Switches connecting various nodes of an interconnection network serve to move data in the network. The switch\u27s delay and throughput impact the overall performance of the network and thus the system. Scheduling efficient movement of data through a switch and configuring the switch to realize a schedule are the main themes of this research. We consider various interconnection network switches including (i) crossbar-based switches, (ii) circuit-switched tree switches, and (iii) fat-tree switches. For crossbar-based input-queued switches, a recent result established that logarithmic packet delay is possible. However, this result assumes that packet transmission time through the switch is no less than schedule-generation time. We prove that without this assumption (as is the case in practice) packet delay becomes linear. We also report results of simulations that bear out our result for practical switch sizes and indicate that a fast scheduling algorithm reduces not only packet delay but also buffer size. We also propose a fast mesh-of-trees based distributed switch scheduling (maximal-matching based) algorithm that has polylog complexity. A circuit-switched tree (CST) can serve as an interconnect structure for various computing architectures and models such as the self-reconfigurable gate array and the reconfigurable mesh. A CST is a tree structure with source and destination processing elements as leaves and switches as internal nodes. We design several scheduling and configuration algorithms that distributedly partition a given set of communications into non-conflicting subsets and then establish switch settings and paths on the CST corresponding to the communications. A fat-tree is another widely used interconnection structure in many of today\u27s high-performance clusters. We embed a reconfigurable mesh inside a fat-tree switch to generate efficient connections. We present an R-Mesh-based algorithm for a fat-tree switch that creates buses connecting input and output ports corresponding to various communications using that switch

A constant time parallel algorithm for the triangularization of a sparse matrix using CD-PARBS

An algorithm for the triangularization of a matrix whose graph is a directed acyclic graph, popularly known as dag, is presented. One of the algorithms for obtaining this special form has been given by Sargent and Westerberg. Their approach is practically good but sequential in nature and cannot be parallelised easily. In this work we present a parallel algorithm which is based on the observation that, if we find the transitive closure matrix of a directed acyclic graph, count the number of entries in each row, sort them in the ascending order of their values and rank them accordingly, we get a lower triangular matrix. We show that all these operations can be done using 3-d CD- PARBS(Complete Directed PARBS) in constant time. The same approach can be used for the block cases, producing the same relabelling as produced by Tarjan’s algorithm, in constant time. To the best of our knowledge, it is the first approach to solve such problems using directed PARBS

On the Design, Analysis, and Implementation of Algorithms for Selected Problems in Graphs and Networks

This thesis studies three problems in network optimization, viz., the minimum spanning tree verification (MSTV) problem, the undirected negative cost cycle detection (UNCCD) problem, and the negative cost girth (NCG) problem. These problems find applications in several domains including program verification, proof theory, real-time scheduling, social networking, and operations research.;The MSTV problem is defined as follows: Given an undirected graph G = (V,E) and a spanning tree T, is T a minimum spanning tree of G? We focus on the case where the number of distinct edge weights is bounded. Using a bucketed data structure to organize the edge weights, we present an efficient algorithm for the MSTV problem, which runs in O (| E| + |V| · K) time, where K is the number of distinct edge weights. When K is a fixed constant, this algorithm runs in linear time. We also profile our MSTV algorithm with the current fastest known MSTV implementation. Our results demonstrate the superiority of our algorithm when K ≤ 24.;The UNCCD problem is defined as follows: Given an undirected graph G = (V,E) with arbitrarily weighted edges, does G contain a negative cost cycle? We discuss two polynomial time algorithms for solving the UNCCD problem: the b-matching approach and the T-join approach. We obtain new results for the case where the edge costs are integers in the range {lcub}--K ·· K{rcub}, where K is a positive constant. We also provide the first extensive empirical study that profiles the discussed UNCCD algorithms for various graph types, sizes, and experiments.;The NCG problem is defined as follows: Given a directed graph G = (V,E) with arbitrarily weighted edges, find the length, or number of edges, of the negative cost cycle having the least number of edges. We discuss three strongly polynomial NCG algorithms. The first NCG algorithm is known as the matrix multiplication approach in the literature. We present two new NCG algorithms that are asymptotically and empirically superior to the matrix multiplication approach for sparse graphs. We also provide a parallel implementation of the matrix multiplication approach that runs in polylogarithmic parallel time using a polynomial number of processors. We include an implementation profile to demonstrate the efficiency of the parallel implementation as we increase the graph size and number of processors. We also present an NCG algorithm for planar graphs that is asymptotically faster than the fastest topology-oblivious algorithm when restricted to planar graphs

Topological Design of Multiple Virtual Private Networks UTILIZING SINK-TREE PATHS

With the deployment of MultiProtocol Label Switching (MPLS) over a core backbone networks, it is possible for a service provider to built Virtual Private Networks (VPNs) supporting various classes of services with QoS guarantees. Efficiently mapping the logical layout of multiple VPNs over a service provider network is a challenging traffic engineering problem. The use of sink-tree (multipoint-to-point) routing paths in a MPLS network makes the VPN design problem different from traditional design approaches where a full-mesh of point-to-point paths is often the choice. The clear benefits of using sink-tree paths are the reduction in the number of label switch paths and bandwidth savings due to larger granularities of bandwidth aggregation within the network. In this thesis, the design of multiple VPNs over a MPLS-like infrastructure network, using sink-tree routing, is formulated as a mixed integer programming problem to simultaneously find a set of VPN logical topologies and their dimensions to carry multi-service, multi-hour traffic from various customers. Such a problem formulation yields a NP-hard complexity. A heuristic path selection algorithm is proposed here to scale the VPN design problem by choosing a small-but-good candidate set of feasible sink-tree paths over which the optimal routes and capacity assignments are determined. The proposed heuristic has clearly shown to speed up the optimization process and the solution can be obtained within a reasonable time for a realistic-size network. Nevertheless, when a large number of VPNs are being layout simultaneously, a standard optimization approach has a limited scalability. Here, the heuristics termed the Minimum-Capacity Sink-Tree Assignment (MCSTA) algorithm proposed to approximate the optimal bandwidth and sink-tree route assignment for multiple VPNs within a polynomial computational time. Numerical results demonstrate the MCSTA algorithm yields a good solution within a small error and sometimes yields the exact solution. Lastly, the proposed VPN design models and solution algorithms are extended for multipoint traffic demand including multipoint-to-point and broadcasting connections