Myung M. Bae

Resource placement in torus-based networks

This paper investigates methods to locate system resources, such as expensive hardware or software modules, to provide the most effective cost/performance trade-offs in a torus parallel machine. This paper contains some solutions to perfect distance-t and perfectiquasi-perfect j-adjacency placement in a k-ary n-cube and a torus using Lee distance error-correcting codes. It also presents generalized resource placement (j-adjacency with distance-t placement) methods based on the concept of covering radius of Lee distance codes.

Edge disjoint Hamiltonian cycles in k-ary n-cubes and hypercubes

Solutions for decomposing a higher dimensional torus to edge disjoint lower dimensional tori, in particular, edge disjoint Hamiltonian cycles are obtained based on the coding theory approach. First, Lee distance Gray codes in Z/sub k//sup n/ are presented and then it is shown how these codes can directly be used to generate edge disjoint Hamiltonian cycles in k-ary n-cubes. Further, some new classes of binary Gray codes are designed from these Lee distance Gray codes and, using these new classes of binary Gray codes, edge disjoint Hamiltonian cycles in hypercubes are generated.

Spare processor allocation for fault tolerance in torus-based multicomputers

Some fault-tolerant architectures use the spare nodes or links to replace the faulty components. This paper gives solutions to spare processor placement problem for torus based networks. Optimal 1-hop spare processor placement methods for multi-dimensional tori and t-hop placement methods for 2D tori are described. In the presence of node failures, a system reconfiguration scheme using spare nodes is also given.

System management in the BlueGene/L supercomputer

The BlueGene/L supercomputer will use system-on-a-chip integration and a highly scalable cellular architecture to deliver 360 teraflops of peak computing power. With 65536 compute nodes, BlueGene/L represents a new level of scalability for parallel systems. As such, it is natural for many scalability challenges to arise. In this paper, we discuss system management and control, including machine booting, software installation, user account management, system monitoring, and job execution. We address the issue of scalability by organizing the system hierarchically. The 65536 compute nodes are organized in 1024 clusters of 64 compute nodes each, called processing sets. Each processing set is under control of a 65th node, called an I/O node. The 1024 processing sets can then be managed to a great extent as a regular Linux cluster, of which there are several successful examples. Regular cluster management is complemented by BlueGene/L specific services, performed by a service node over a separate control network. Our software development and experiments have been conducted so far using an architecturally accurate simulator of BlueGene/L, and we are gearing up to test real prototypes in 2003.

Gray codes for torus and edge disjoint Hamiltonian cycles

Lee distance Gray codes for k-ary n-cubes and torus networks are presented. Using these Lee distance Gray codes, it is further shown how to directly generate edge disjoint Hamiltonian cycles for a class of k-ary n-cubes, 2-D tori, and hypercubes.

Edge-disjoint Hamiltonian cycles in two-dimensional torus

The torus is one of the popular topologies for the interconnecting processors to build high-performance multicomputers. This paper presents methods to generate edge-disjoint Hamiltonian cycles in 2D tori.

Semi-hierarchical approach for reliability, availability, and serviceability of cellular systems

INTRODUCTION Cellular architectures offer a path to building very large parallel systems, with thousands of processors,that offer superior price/performance when compared to more conventional parallel systems like the IBM RS/6000 SP and PC clusters. However, those large scale cellular machines introduce significant system management challenges. In particular, the ability to track and analyze every possible fault condition, whether transient (soft) or permanent (hard), [1] in large cellular machines is a major issue from systems software, hardware and architecture point of view.

Data Rearrangement between Radix-k and Lee Distance Gray Codes in k-ary n-cubes

The k-ary n-cube is one of the popular topologies for interconnecting processors in multicomputers. This paper studies the difference in communication requirements between two Lee distance Gray codes when moving data from processors in normal radix k order to those in Gray code order in k -ary n-cube networks. Algorithms for k-ary to Gray code conversion, and vice versa, in k-ary n-cube networks are described under various channel constraints, i.e., one-port and all-port communication assumptions. The minimum length path routing algorithm for nonreflective Gray code requires roughly M(k/4) and (n?1)M(k/4) steps for data element transfers under all-port communication and one-port communication, respectively, for M elements per node. It is also shown that using a nonminimum length path routing algorithm, the number of steps for data element transfers can be halved. Lower bounds for the number of element transfers are derived, and the proposed algorithm using nonminimum length paths under one-port communication is shown to be near optimal.

On independent set of Lee distance Gray codes

In a Gray code C, the set of k/sup n/ vectors over Z/sub k//sup n/ is arranged in a sequence such that two adjacent vectors are at a Lee distance one. It is assumed that the first and the last vectors in this sequence are also at a distance 1. Two Gray codes, C/sub 1/ and C/sub 2/, over Z/sub k//sup n/ are said to be independent if two words, a and b, are adjacent in C/sub 1/ (or C/sub 2/), then they are not adjacent in C/sub 2/ (or C/sub 1/). If k/spl ges/3, we can have at most n sets of independent Gray codes; for k=2, this number is [n/2].