Multistage interconnection networks : improved routing algorithms and fault tolerance

Multistage interconnection networks for use by multiprocessor systems are optimal in terms of the number of switching element, but the routing algorithms used to set up these networks are suboptimal in terms of time. The network set-up time and reliability are the major factors to affect the performance of multistage interconnection networks. This work improves routing on Benes and Clos networks as well as the fault tolerant capability. The permutation representation is examined as well as the Clos and Benes networks. A modified edge coloring algorithm is applied to the regular bipartite multigraph which represents a Clos network. The looping and parallel looping algorithms are examined and a modified Tree-Connected Computer is adopted to execute a bidirectional parallel looping algorithm for Benes networks. A new fault tolerant Clos network is presented

On chip interconnects for multiprocessor turbo decoding architectures

International audienc

Answering Spatial Multiple-Set Intersection Queries Using 2-3 Cuckoo Hash-Filters

We show how to answer spatial multiple-set intersection queries in O(n(log w)/w + kt) expected time, where n is the total size of the t sets involved in the query, w is the number of bits in a memory word, k is the output size, and c is any fixed constant. This improves the asymptotic performance over previous solutions and is based on an interesting data structure, known as 2-3 cuckoo hash-filters. Our results apply in the word-RAM model (or practical RAM model), which allows for constant-time bit-parallel operations, such as bitwise AND, OR, NOT, and MSB (most-significant 1-bit), as exist in modern CPUs and GPUs. Our solutions apply to any multiple-set intersection queries in spatial data sets that can be reduced to one-dimensional range queries, such as spatial join queries for one-dimensional points or sets of points stored along space-filling curves, which are used in GIS applications.Comment: Full version of paper from 2017 ACM SIGSPATIAL International Conference on Advances in Geographic Information System

Crosstalk-free Conjugate Networks for Optical Multicast Switching

High-speed photonic switching networks can switch optical signals at the rate of several terabits per second. However, they suffer from an intrinsic crosstalk problem when two optical signals cross at the same switch element. To avoid crosstalk, active connections must be node-disjoint in the switching network. In this paper, we propose a sequence of decomposition and merge operations, called conjugate transformation, performed on each switch element to tackle this problem. The network resulting from this transformation is called conjugate network. By using the numbering-schemes of networks, we prove that if the route assignments in the original network are link-disjoint, their corresponding ones in the conjugate network would be node-disjoint. Thus, traditional nonblocking switching networks can be transformed into crosstalk-free optical switches in a routine manner. Furthermore, we show that crosstalk-free multicast switches can also be obtained from existing nonblocking multicast switches via the same conjugate transformation.Comment: 10 page

Succinct Representations of Permutations and Functions

We investigate the problem of succinctly representing an arbitrary permutation, \pi, on {0,...,n-1} so that \pi^k(i) can be computed quickly for any i and any (positive or negative) integer power k. A representation taking (1+\epsilon) n lg n + O(1) bits suffices to compute arbitrary powers in constant time, for any positive constant \epsilon <= 1. A representation taking the optimal \ceil{\lg n!} + o(n) bits can be used to compute arbitrary powers in O(lg n / lg lg n) time. We then consider the more general problem of succinctly representing an arbitrary function, f: [n] \rightarrow [n] so that f^k(i) can be computed quickly for any i and any integer power k. We give a representation that takes (1+\epsilon) n lg n + O(1) bits, for any positive constant \epsilon <= 1, and computes arbitrary positive powers in constant time. It can also be used to compute f^k(i), for any negative integer k, in optimal O(1+|f^k(i)|) time. We place emphasis on the redundancy, or the space beyond the information-theoretic lower bound that the data structure uses in order to support operations efficiently. A number of lower bounds have recently been shown on the redundancy of data structures. These lower bounds confirm the space-time optimality of some of our solutions. Furthermore, the redundancy of one of our structures "surpasses" a recent lower bound by Golynski [Golynski, SODA 2009], thus demonstrating the limitations of this lower bound.Comment: Preliminary versions of these results have appeared in the Proceedings of ICALP 2003 and 2004. However, all results in this version are improved over the earlier conference versio

An efficient sparse conjugate gradient solver using a Beneš permutation network

© 2014 Technical University of Munich (TUM).The conjugate gradient (CG) is one of the most widely used iterative methods for solving systems of linear equations. However, parallelizing CG for large sparse systems is difficult due to the inherent irregularity in memory access pattern. We propose a novel processor architecture for the sparse conjugate gradient method. The architecture consists of multiple processing elements and memory banks, and is able to compute efficiently both sparse matrix-vector multiplication, and other dense vector operations. A Beneš permutation network with an optimised control scheme is introduced to reduce memory bank conflicts without expensive logic. We describe a heuristics for offline scheduling, the effect of which is captured in a parametric model for estimating the performance of designs generated from our approach

Upper Bound Analysis and Routing in Optical Benes Networks

Multistage Interconnection Networks (MIN) are popular in switching and communication applications. It has been used in telecommunication and parallel computing systems for many years. The new challenge facing optical MIN is crosstalk, which is caused by coupling two signals within a switching element. Crosstalk is not too big an issue in the Electrical Domain, but due to the stringent Bit Error Rate (BER) constraint, it is a big major concern in the Optical Domain. In this research dissertation, we will study the blocking probability in the optical network and we will study the deterministic conditions for strictly non-blocking Vertical Stacked Optical Benes Networks (VSOBN) with and without worst-case scenarios. We will establish the upper bound on blocking probability of Vertical Stacked Optical Benes Networks with respect to the number of planes used when the non-blocking requirement is not met. We will then study routing in WDM Benes networks and propose a new routing algorithm so that the number of wavelengths can be reduced. Since routing in WDM optical network is an NP-hard problem, many heuristic algorithms are designed by many researchers to perform this routing. We will also develop a genetic algorithm, simulated annealing algorithm and ant colony technique and apply these AI algorithms to route the connections in WDM Benes network