33 research outputs found
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Interconnection Networks Based on Gaussian and Eisenstein-Jacobi Integers
Quotient rings of Gaussian and Eisenstein-Jacobi(EJ) integers can be deployed to construct interconnection networks with good topological properties. In this thesis, we propose deadlock-free deterministic and partially adaptive routing algoÂrithms for hexagonal networks, one special class of EJ networks. Then we discuss higher dimensional Gaussian networks as an alternative to classical multidimenÂsional toroidal networks. For this topology, we explore many properties including distance distribution and the decomposition of higher dimensional Gaussian net works into Hamiltonian cycles. In addition, we propose some efficient communiÂcation algorithms for higher dimensional Gaussian networks including one-to-all broadcasting and shortest path routing. Simulation results show that the routÂing algorithm proposed for higher dimensional Gaussian networks outperforms the routing algorithm of the corresponding torus networks with approximately the same number of nodes. These simulation results are expected since higher dimenÂsional Gaussian networks have a smaller diameter and a smaller average message latency as compared with toroidal networks.
Finally, we introduce a degree-three interconnection network obtained from pruning a Gaussian network. This network shows possible performance improveÂment over other degree-three networks since it has a smaller diameter compared to other degree-three networks. Many topological properties of degree-three pruned Gaussian network are explored. In addition, an optimal shortest path routing algorithm and a one-to-all broadcasting algorithm are given
Multiple Bus Networks for Binary -Tree Algorithms.
Multiple bus networks (MBN) connect processors via buses. This dissertation addresses issues related to running binary-tree algorithms on MBNs. These algorithms are of a fundamental nature, and reduce inputs at leaves of a binary tree to a result at the root. We study the relationships between running time, degree (maximum number of connections per processor) and loading (maximum number of connections per bus). We also investigate fault-tolerance, meshes enhanced with MBNs, and VLSI layouts for binary-tree MBNs. We prove that the loading of optimal-time, degree-2, binary-tree MBNs is non-constant. In establishing this result, we derive three loading lower bounds Wn , W&parl0;n23&parr0; and W&parl0;nlogn&parr0; , each tighter than the previous one. We also show that if the degree is increased to 3, then the loading can be a constant. A constant loading degree-2 MBN exists, if the algorithm is allowed to run slower than the optimal. We introduce a new enhanced mesh architecture (employing binary-tree MBNs) that captures features of all existing enhanced meshes. This architecture is more flexible, allowing all existing enhanced mesh results to be ported to a more implementable platform. We present two methods for imparting tolerance to bus and processor faults in binary-tree MBNs. One of the methods is general, and can be used with any MBN and for both processor and bus faults. A key feature of this method is that it permits the network designer to designate a set of buses as unimportant and consider all faulty buses as unimportant. This minimizes the impact of faulty elements on the MBN. The second method is specific to bus faults in binary-tree MBNs, whose features it exploits to produce faster solutions. We also derive a series of results that distill the lower bound on the perimeter layout area of optimal-time, binary-tree MBNs to a single conjecture. Based on this we believe that optimal-time, binary-tree MBNs require no less area than a balanced tree topology even though such MBNs can reuse buses over various steps of the algorithm
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
Algebraic Topology for Data Scientists
This book gives a thorough introduction to topological data analysis (TDA),
the application of algebraic topology to data science. Algebraic topology is
traditionally a very specialized field of math, and most mathematicians have
never been exposed to it, let alone data scientists, computer scientists, and
analysts. I have three goals in writing this book. The first is to bring people
up to speed who are missing a lot of the necessary background. I will describe
the topics in point-set topology, abstract algebra, and homology theory needed
for a good understanding of TDA. The second is to explain TDA and some current
applications and techniques. Finally, I would like to answer some questions
about more advanced topics such as cohomology, homotopy, obstruction theory,
and Steenrod squares, and what they can tell us about data. It is hoped that
readers will acquire the tools to start to think about these topics and where
they might fit in.Comment: 322 pages, 69 figures, 5 table
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Using MapReduce Streaming for Distributed Life Simulation on the Cloud
Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp
Pattern Recognition
A wealth of advanced pattern recognition algorithms are emerging from the interdiscipline between technologies of effective visual features and the human-brain cognition process. Effective visual features are made possible through the rapid developments in appropriate sensor equipments, novel filter designs, and viable information processing architectures. While the understanding of human-brain cognition process broadens the way in which the computer can perform pattern recognition tasks. The present book is intended to collect representative researches around the globe focusing on low-level vision, filter design, features and image descriptors, data mining and analysis, and biologically inspired algorithms. The 27 chapters coved in this book disclose recent advances and new ideas in promoting the techniques, technology and applications of pattern recognition