Algorithms



On the Bottleneck Structure of Congestion-Controlled Networks



Publication Source: ACM SIGMETRICS 2020, Boston MA; Proc. ACM Meas. Anal. Comput. Syst., Vol. 3, No. 3, Article 59, December 2019

In this paper, we introduce the Theory of Bottleneck Ordering, a mathematical framework that reveals the bottleneck structure of data networks. This theoretical framework provides insights into the inherent topological properties of a network at least in three areas: (1) It identifies the regions of influence of each bottleneck; (2) it reveals the order in which bottlenecks (and flows traversing them) converge to their steady state transmission rates in distributed congestion control algorithms; and (3) it provides key insights to the design of optimized traffic engineering policies. We demonstrate the efficacy of the proposed theory in TCP congestion-controlled networks for two broad classes of algorithms: congestion-based algorithms (BBR) and loss-based additive-increase/multiplicative-decrease algorithms (Cubic and Reno). Among other results, our network experiments show that: (1) Qualitatively, both classes of congestion control algorithms behave as predicted by the bottleneck structure of the network; (2) flows compete for bandwidth only with other flows operating at the same bottleneck level; (3) BBR flows achieve higher performance and fairness than Cubic and Reno flows due to their ability to operate at the right bottleneck level; (4) the bottleneck structure of a network is ever-changing and its levels can be folded due to variations in the flows’ round trip times; and (5) against conventional wisdom, low-hitter flows can have a large impact to the overall performance of a network. This paper has not yet been published. If you would like to receive a copy once available, please contact us or check back here in December.

G2: A Network Optimization Framework for High-Precision Analysis of Bottleneck and Flow Performance



Publication Source: 2019 IEEE/ACM SuperComputing Conference, Innovating the Network for Data-Intensive Science (INDIS) Workshop, Denver, CO

Congestion control algorithms for data networks have been the subject of intense research for the last three decades. While most of the work has focused around the characterization of a flow’s bottleneck link, understanding the interactions amongst links and the ripple effects that perturbations in a link can cause on the rest of the network has remained much less understood. The Theory of Bottleneck Ordering is a recently developed mathematical framework that reveals the bottleneck structure of a network and provides a model to understand such effects. In this paper we present G2, the first operational network optimization framework that utilizes this new theoretical framework to characterize with high-precision the performance of bottlenecks and flows. G2 generates an interactive graph structure that describes how perturbations in links and flows propagate, providing operators new optimization insights and traffic engineering recommendations to help improve network performance. We provide a description of the G2 implementation and a set of experiments using real TCP/IP code to demonstrate its operational efficacy.

This paper has not yet been published. If you would like to receive a copy once available, please contact us or check back here after the 2019 SuperComputing Conference. For more information on G2 technology, visit https://www.reservoir.com/research/tech/networking/.


Fast and Scalable Distributed Tensor Decompositions



Publication Source: IEEE High Performance Extreme Computing Conference (HPEC) 2019, Waltham, MA

Tensor decomposition is a prominent technique for analyzing multi-attribute data and is being increasingly used for data analysis in different application areas. Tensor decomposition methods are computationally intense and often involve irregular memory accesses over large-scale sparse data. Hence it becomes critical to optimize the execution of such data intensive computations and associated data movement to reduce the eventual time-to-solution in data analysis applications. With the prevalence of using advanced high-performance computing (HPC) systems for data analysis applications, it is becoming increasingly important to provide fast and scalable implementation of tensor decompositions and execute them efficiently on modern and advanced HPC systems. In this paper, we present distributed tensor decomposition methods that achieve faster, memory-efficient, and communication-reduced execution on HPC systems. We demonstrate that our techniques reduce the overall communication and execution time of tensor decomposition methods when they are used for analyzing datasets of varied size from real application. We illustrate our results on HPE Superdome Flex server, a high-end modular system offering large-scale in-memory computing, and on a distributed cluster of Intel Xeon multi-core nodes.
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Fast Large-Scale Algorithm for Electromagnetic Wave Propagation in 3D Media



Publication Source: IEEE High Performance Extreme Computing Conference (HPEC) 2019, Waltham, MA

We present a fast, large-scale algorithm for the simulation of electromagnetic waves (Maxwell’s equations) in three-dimensional inhomogeneous media. The algorithm has a complexity of O(N log(N)) and runs in parallel. Numerical simulations show the rapid treatment of problems with tens of millions of unknowns on a small shared-memory cluster ( 16 cores).
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Combinatorial Multigrid: Advanced Preconditioners For Ill-Conditioned Linear Systems



Publication Source: IEEE High Performance Extreme Computing Conference (HPEC) 2019, Waltham, MA

The Combinatorial Multigrid (CMG) technique is a practical and adaptable solver and combinatorial preconditioner for solving certain classes of large, sparse systems of linear equations. CMG is similar to Algebraic Multigrid (AMG) but replaces large groupings of fine-level variables with a single coarse-level one, resulting in simple and fast interpolation schemes. These schemes further provide control over the refinement strategies at different levels of the solver hierarchy depending on the condition number of the system being solved [1]. While many pre-existing solvers may be able to solve large, sparse systems with relatively low complexity, inversion may require O(n2) space; whereas, if we know that a linear operator has ~n = O(n) nonzero elements, we desire to use O(n) space in order to reduce communication as much as possible. Being able to invert sparse linear systems of equations, asymptotically as fast as the values can be read from memory, has been identified by the Defense Advanced Research Projects Agency (DARPA) and the Department of Energy (DOE) as increasingly necessary for scalable solvers and energy-efficient algorithms [2], [3] in scientific computing. Further, as industry and government agencies move towards exascale, fast solvers and communicationavoidance will be more necessary [4], [5]. In this paper, we present an optimized implementation of the Combinatorial Multigrid in C using Petsc and analyze the solution of various systems using the CMG approach as a preconditioner on much larger problems than have been presented thus far. We compare the number of iterations, setup times and solution times against other popular preconditioners for such systems, including Incomplete Cholesky and a Multigrid approach in Petsc against common problems, further exhibiting superior performance by the CMG. 1 2 Index Terms—combinatorial algorithms, spectral support solver, linear systems, fast solvers, preconditioners, multigrid, graph laplacian, benchmarking, iterative solvers
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