S. Lakshmivarahan

Symmetry in interconnection networks based on Cayley graphs of permutation groups: A survey☆

Abstract This survey provides a comprehensive and unified analysis of symmetry in a wide variety of Cayley graphs of permutation groups. These include the star graph, bubble-sort graph, modified bubble-sort graph, complete-transposition graph, prefix-reversal graph, alternating-group graph, binary and base-b (b ≥ 3) hypercube, cube connected cycles, bisectional graph, folded hypercube and binary orthogonal graph. In addition, we also define a variety of generalizations of the hypercube and orthogonal graphs. The types of symmetry analyzed include vertex and edge transitivity, distance regularity and distance transitivity. Since these notions of symmetry depend on the shortest paths, as a by product we also describe the shortest path routing algorithms for these graphs. We present a number of open problems related to the networks described in this paper.

EMBEDDING OF CYCLES AND GRIDS IN STAR GRAPHS

The use of the star graph as a viable interconnection scheme for parallel computers has been examined by a number of authors in recent times. An attractive feature of this class of graphs is that it has sublogarithmic diameter and has a great deal of symmetry akin to the binary hypercube. In this paper we describe a new class of algorithms for embedding (a) Hamiltonian cycle (b) the set of all even cycles and (c) a variety of two- and multi-dimensional grids in a star graph. In addition, we also derive an algorithm for the ranking and the unranking problem with respect to the Hamiltonian cycle.

A new class of interconnection networks based on the alternating group

This paper introduces a new class of interconnection scheme based on the Cayley graph of the alternating group. It is shown that this class of graphs are edge symmetric and 2-transitive. We then describe an algorithm for (a) packet routing based on the shortest path analysis, (b) finding a Hamiltonian cycle, (c) ranking and unranking along the chosen Hamiltonian cycle, (d) unit expansion and dilation three embedding of a class of two-dimensional grids, (e) unit dilation embedding of a variety of cycles, and (f) algorithm for broadcasting messages. The paper concludes with a short analysis of contention resulting from a typical communication scheme. Although this class of graphs does not possess many of the symmetry properties of the binary hypercube, with respect to the one source broadcasting, these graphs perform better than does a hypercube, and with respect to the contention problem, these graphs perform better than do the star graphs and are close to the hypercube.

Embedding of cycles and grids in star graphs

The use of star graphs as a viable interconnection scheme for parallel computers has been examined by a number of authors. An attractive feature of this class of graphs is that it has sublogarithmic diameter and has a great deal of symmetry akin to the binary hypercube. The authors describe a new class of algorithms for embedding Hamiltonian cycle, the set of all even cycles and a variety of two and multi-dimensional grids in a star graph. They derive an algorithm for the ranking and the unranking problem with respect to the Hamiltonian cycle.<<ETX>>

A new hierarchy of hypercube interconnection schemes for parallel computers

This paper introduces a new hierarchy of cube-based interconnection schemes, called the base-b cube (which properly contains the well-known binary cube), for the design of parallel computers. This hierarchy admits a recursive definition and allows many more reconfigurations than are possible with the binary cube. Our analysis addresses the inherent cost-delay trade-off for this hierarchy along with a number of related topological properties such as sparsity, diameter, existence of node disjoint paths, and odd and even cycles. Embeddings of standard interconnection schemes including linear and two-dimensional arrays, rings, and complete binary trees in a base-b cube are illustrated.

Cluster analysis of multimodel ensemble data from SAMEX

Abstract Short-range ensemble forecasts from the Storm and Mesoscale Ensemble Experiment (SAMEX) are examined to explore the importance of model diversity in short-range ensemble forecasting systems. Two basic techniques from multivariate data analysis are used: cluster analysis and principal component analysis. This 25-member ensemble is constructed of 36-h forecasts from four different numerical weather prediction models, including the Eta Model, the Regional Spectral Model (RSM), the Advanced Regional Prediction System (ARPS), and the Pennsylvania State University–National Center for Atmospheric Research fifth-generation Mesoscale Model (MM5). The Eta Model and RSM forecasts are initialized using the breeding of growing modes approach, the ARPS model forecasts are initialized using a scaled lagged average forecasting approach, and the MM5 forecasts are initialized using a random coherent structures approach. The MM5 forecasts also include different model physical parameterization schemes, allowing us t...

PROJECT CRAFT A Real-Time Delivery System for Nexrad Level II Data Via The Internet

Abstract The NOAA NWS announced at the annual meeting of the American Meteorological Society in February 2003 its intent to create an Internet-based pseudo-operational system for delivering Weather Surveillance Radar-1988 Doppler (WSR-88D) Level II data. In April 2004, the NWS deployed the Next-Generation Weather Radar (NEXRAD) level II central collection functionality and set up a framework for distributing these data. The NWS action was the direct result of a successful joint government, university, and private sector development and test effort called the Collaborative Radar Acquisition Field Test (CRAFT) project. Project CRAFT was a multi-institutional effort among the Center for Analysis and Prediction of Storms, the University Corporation for Atmospheric Research, the University of Washington, and the three NOAA organizations, National Severe Storms Laboratory, WSR-88D Radar Operations Center (ROC), and National Climatic Data Center. The principal goal of CRAFT was to demonstrate the real-time compr...

Ring, torus and hypercube architectures/algorithms for parallel computing

Abstract This paper provides a survey of both architectural and algorithmic aspects of solving problems using parallel processors with ring, torus and hypercube interconnection.

Parallel sorting algorithms

Publisher Summary This chapter presents a survey on various parallel sorting algorithms. Sorting is a nontrivial problem and has widespread commercial and business applications. Serial algorithms for sorting have been available since the days of punched-card machines. At present, there is a considerable body of literature on serial sorting algorithms. Parallel algorithms for sorting are of a recent origin and came into existence over the past decade. The chapter presents a unified treatment of various parallel sorting algorithms by bringing out clearly the relation between the architecture of parallel computers and the structure of algorithms. In the design of parallel algorithms in general, and of parallel sorting algorithms in particular, two models have been widely used: (1) models based on fixed interconnection networks such as the same or single instruction on multiple data (SIMD) machine mesh-connected network and (2) models based on a global memory, which is shared by various processors. The special-purpose network-sorting algorithms are described. Algorithms for SIMD machines are given.

Efficient algorithms for finding depth-first and breadth-first search trees in permutation graphs

This paper presents an O(n log log n) time algorithm for finding a depth-first search tree and an O(n) time algorithm for finding a breadth-first search tree in a permutation graph, respectively.