Optimal Networks from Error Correcting Codes

To address growth challenges facing large Data Centers and supercomputing clusters a new construction is presented for scalable, high throughput, low latency networks. The resulting networks require 1.5-5 times fewer switches, 2-6 times fewer cables, have 1.2-2 times lower latency and correspondingly lower congestion and packet losses than the best present or proposed networks providing the same number of ports at the same total bisection. These advantage ratios increase with network size. The key new ingredient is the exact equivalence discovered between the problem of maximizing network bisection for large classes of practically interesting Cayley graphs and the problem of maximizing codeword distance for linear error correcting codes. Resulting translation recipe converts existent optimal error correcting codes into optimal throughput networks.Comment: 14 pages, accepted at ANCS 2013 conferenc

A study of the communication cost of the FFT on torus multicomputers

The computation of a one-dimensional FFT on a c-dimensional torus multicomputer is analyzed. Different approaches are proposed which differ in the way they use the interconnection network. The first approach is based on the multidimensional index mapping technique for the FFT computation. The second approach starts from a hypercube algorithm and then embeds the hypercube onto the torus. The third approach reduces the communication cost of the hypercube algorithm by pipelining the communication operations. A novel methodology to pipeline the communication operations on a torus is proposed. Analytical models are presented to compare the different approaches. This comparison study shows that the best approach depends on the number of dimensions of the torus and the communication start-up and transfer times. The analytical models allow us to select the most efficient approach for the available machine.Peer ReviewedPostprint (published version

A communication model of broadcast in wormhole-routed networks on-chip

This paper presents a novel analytical model to compute communication latency of broadcast as the most fundamental collective communication operation. The novelty of the model lies in its ability to predict the broadcast communication latency in wormhole-routed architectures employing asynchronous multi-port routers scheme. The model is applied to the Quarc NoC and its validity is verified by comparing the model predictions against the results obtained from a discrete-event simulator developed using OMNET++

A performance model of multicast communication in wormhole-routed networks on-chip

Collective communication operations form a part of overall traffic in most applications running on platforms employing direct interconnection networks. This paper presents a novel analytical model to compute communication latency of multicast as a widely used collective communication operation. The novelty of the model lies in its ability to predict the latency of the multicast communication in wormhole-routed architectures employing asynchronous multi-port routers scheme. The model is applied to the Quarc NoC and its validity is verified by comparing the model predictions against the results obtained from a discrete-event simulator developed using OMNET++

Performance modeling of fault-tolerant circuit-switched communication networks

Circuit switching (CS) has been suggested as an efficient switching method for supporting simultaneous communications (such as data, voice, and images) across parallel systems due to its ability to preserve both communication performance and fault-tolerant demands in such systems. In this paper we present an efficient scheme to capture the mean message latency in 2D torus with CS in the presence of faulty components. We have also conducted extensive simulation experiments, the results of which are used to validate the analytical mode

A Novel Indexing Method for Improving Timeliness of High-Dimensional Data

Investment in information technology (IT) has been growing rapidly and one key reason for investing in IT is to improve information quality (IQ). Timeliness is an important IQ dimension that often needs to be improved for decision making. Especially in the era of big data, timeliness becomes more valued because of challenges of massive data size and high dimensionality. Many financial analyses require timely data to support time-critical decision making. In this paper, we develop a novel index method and effective query algorithms to reduce latency of querying high-dimensional data. The effectiveness of point, range, and similarity queries implemented using our methods is evaluated using a high-dimensional testbed conducted using real world financial data. Results show that our method outperforms existing methods in query speed of three types of queries frequently used in financial decision making

Stochastic Analysis of a Churn-Tolerant Structured Peer-to-Peer Scheme

We present and analyze a simple and general scheme to build a churn (fault)-tolerant structured Peer-to-Peer (P2P) network. Our scheme shows how to "convert" a static network into a dynamic distributed hash table(DHT)-based P2P network such that all the good properties of the static network are guaranteed with high probability (w.h.p). Applying our scheme to a cube-connected cycles network, for example, yields a $O(\log N)$ degree connected network, in which every search succeeds in $O(\log N)$ hops w.h.p., using $O(\log N)$ messages, where $N$ is the expected stable network size. Our scheme has an constant storage overhead (the number of nodes responsible for servicing a data item) and an $O(\log N)$ overhead (messages and time) per insertion and essentially no overhead for deletions. All these bounds are essentially optimal. While DHT schemes with similar guarantees are already known in the literature, this work is new in the following aspects: (1) It presents a rigorous mathematical analysis of the scheme under a general stochastic model of churn and shows the above guarantees; (2) The theoretical analysis is complemented by a simulation-based analysis that validates the asymptotic bounds even in moderately sized networks and also studies performance under changing stable network size; (3) The presented scheme seems especially suitable for maintaining dynamic structures under churn efficiently. In particular, we show that a spanning tree of low diameter can be efficiently maintained in constant time and logarithmic number of messages per insertion or deletion w.h.p. Keywords: P2P Network, DHT Scheme, Churn, Dynamic Spanning Tree, Stochastic Analysis