Data Structures
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Application of TRIE Data Structure and Corresponding Associative Algorithms for Process Optimization in GRID Environment
Application of TRIE data structure and corresponding associative algorithms for process optimization in GRID environment V. V. Kashanskya, I. L. Kaftannikovb South Ural State University (National Research University), 76, Lenin prospekt, Chelyabinsk, 454080, Russia E-mail: a [email protected], b [email protected] Growing interest around different BOINC powered projects made volunteer GRID model widely used last years, arranging lots of computational resources in different environments. There are many revealed problems of Big Data and horizontally scalable multiuser systems. This paper provides an analysis of TRIE data structure and possibilities of its application in contemporary volunteer GRID networks, including routing (L3 OSI) and spe- cialized key-value storage engine (L7 OSI). The main goal is to show how TRIE mechanisms can influence de- livery process of the corresponding GRID environment resources and services at different layers of networking abstraction. The relevance of the optimization topic is ensured by the fact that with increasing data flow intensi- ty, the latency of the various linear algorithm based subsystems as well increases. This leads to the general ef- fects, such as unacceptably high transmission time and processing instability. Logically paper can be divided into three parts with summary. The first part provides definition of TRIE and asymptotic estimates of corresponding algorithms (searching, deletion, insertion). The second part is devoted to the problem of routing time reduction by applying TRIE data structure. In particular, we analyze Cisco IOS switching services based on Bitwise TRIE and 256 way TRIE data structures. The third part contains general BOINC architecture review and recommenda- tions for highly-loaded projects. -
Lecture 11: Heapsort & Its Analysis
Lecture 11: Heapsort & Its Analysis Agenda: • Heap recall: – Heap: definition, property – Max-Heapify – Build-Max-Heap • Heapsort algorithm • Running time analysis Reading: • Textbook pages 127 – 138 1 Lecture 11: Heapsort (Binary-)Heap data structure (recall): • An array A[1..n] of n comparable keys either ‘≥’ or ‘≤’ • An implicit binary tree, where – A[2j] is the left child of A[j] – A[2j + 1] is the right child of A[j] j – A[b2c] is the parent of A[j] j • Keys satisfy the max-heap property: A[b2c] ≥ A[j] • There are max-heap and min-heap. We use max-heap. • A[1] is the maximum among the n keys. • Viewing heap as a binary tree, height of the tree is h = blg nc. Call the height of the heap. [— the number of edges on the longest root-to-leaf path] • A heap of height k can hold 2k —— 2k+1 − 1 keys. Why ??? Since lg n − 1 < k ≤ lg n ⇐⇒ n < 2k+1 and 2k ≤ n ⇐⇒ 2k ≤ n < 2k+1 2 Lecture 11: Heapsort Max-Heapify (recall): • It makes an almost-heap into a heap. • Pseudocode: procedure Max-Heapify(A, i) **p 130 **turn almost-heap into a heap **pre-condition: tree rooted at A[i] is almost-heap **post-condition: tree rooted at A[i] is a heap lc ← leftchild(i) rc ← rightchild(i) if lc ≤ heapsize(A) and A[lc] > A[i] then largest ← lc else largest ← i if rc ≤ heapsize(A) and A[rc] > A[largest] then largest ← rc if largest 6= i then exchange A[i] ↔ A[largest] Max-Heapify(A, largest) • WC running time: lg n. -
CS 106X, Lecture 21 Tries; Graphs
CS 106X, Lecture 21 Tries; Graphs reading: Programming Abstractions in C++, Chapter 18 This document is copyright (C) Stanford Computer Science and Nick Troccoli, licensed under Creative Commons Attribution 2.5 License. All rights reserved. Based on slides created by Keith Schwarz, Julie Zelenski, Jerry Cain, Eric Roberts, Mehran Sahami, Stuart Reges, Cynthia Lee, Marty Stepp, Ashley Taylor and others. Plan For Today • Tries • Announcements • Graphs • Implementing a Graph • Representing Data with Graphs 2 Plan For Today • Tries • Announcements • Graphs • Implementing a Graph • Representing Data with Graphs 3 The Lexicon • Lexicons are good for storing words – contains – containsPrefix – add 4 The Lexicon root the art we all arts you artsy 5 The Lexicon root the contains? art we containsPrefix? add? all arts you artsy 6 The Lexicon S T A R T L I N G S T A R T 7 The Lexicon • We want to model a set of words as a tree of some kind • The tree should be sorted in some way for efficient lookup • The tree should take advantage of words containing each other to save space and time 8 Tries trie ("try"): A tree structure optimized for "prefix" searches struct TrieNode { bool isWord; TrieNode* children[26]; // depends on the alphabet }; 9 Tries isWord: false a b c d e … “” isWord: true a b c d e … “a” isWord: false a b c d e … “ac” isWord: true a b c d e … “ace” 10 Reading Words Yellow = word in the trie A E H S / A E H S A E H S A E H S / / / / / / / / A E H S A E H S A E H S A E H S / / / / / / / / / / / / A E H S A E H S A E H S / / / / / / / -
Vertex Coloring
Lecture 1 Vertex Coloring 1.1 The Problem Nowadays multi-core computers get more and more processors, and the question is how to handle all this parallelism well. So, here's a basic problem: Consider a doubly linked list that is shared by many processors. It supports insertions and deletions, and there are simple operations like summing up the size of the entries that should be done very fast. We decide to organize the data structure as an array of dynamic length, where each array index may or may not hold an entry. Each entry consists of the array indices of the next entry and the previous entry in the list, some basic information about the entry (e.g. its size), and a pointer to the lion's share of the data, which can be anywhere in the memory. Memory structure Logical structure 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 next previous size data Figure 1.1: Linked listed after initialization. Blue links are forward pointers, red links backward pointers (these are omitted from now on). We now can quickly determine the total size by reading the array in one go from memory, which is quite fast. However, how can we do insertions and deletions fast? These are local operations affecting only one list entry and the pointers of its \neighbors," i.e., the previous and next list element. We want to be able to do many such operations concurrently, by different processors, while maintaining the link structure! Being careless and letting each processor act independently invites desaster, see Figure 1.3. -
Introduction to Linked List: Review
Introduction to Linked List: Review Source: http://www.geeksforgeeks.org/data-structures/linked-list/ Linked List • Fundamental data structures in C • Like arrays, linked list is a linear data structure • Unlike arrays, linked list elements are not stored at contiguous location, the elements are linked using pointers Array vs Linked List Why Linked List-1 • Advantages over arrays • Dynamic size • Ease of insertion or deletion • Inserting a new element in an array of elements is expensive, because room has to be created for the new elements and to create room existing elements have to be shifted For example, in a system if we maintain a sorted list of IDs in an array id[]. id[] = [1000, 1010, 1050, 2000, 2040] If we want to insert a new ID 1005, then to maintain the sorted order, we have to move all the elements after 1000 • Deletion is also expensive with arrays until unless some special techniques are used. For example, to delete 1010 in id[], everything after 1010 has to be moved Why Linked List-2 • Drawbacks of Linked List • Random access is not allowed. • Need to access elements sequentially starting from the first node. So we cannot do binary search with linked lists • Extra memory space for a pointer is required with each element of the list Representation in C • A linked list is represented by a pointer to the first node of the linked list • The first node is called head • If the linked list is empty, then the value of head is null • Each node in a list consists of at least two parts 1. -
Easy PRAM-Based High-Performance Parallel Programming with ICE∗
Easy PRAM-based high-performance parallel programming with ICE∗ Fady Ghanim1, Uzi Vishkin1,2, and Rajeev Barua1 1Electrical and Computer Engineering Department 2University of Maryland Institute for Advance Computer Studies University of Maryland - College Park MD, 20742, USA ffghanim,barua,[email protected] Abstract Parallel machines have become more widely used. Unfortunately parallel programming technologies have advanced at a much slower pace except for regular programs. For irregular programs, this advancement is inhibited by high synchronization costs, non-loop parallelism, non-array data structures, recursively expressed parallelism and parallelism that is too fine-grained to be exploitable. We present ICE, a new parallel programming language that is easy-to-program, since: (i) ICE is a synchronous, lock-step language; (ii) for a PRAM algorithm its ICE program amounts to directly transcribing it; and (iii) the PRAM algorithmic theory offers unique wealth of parallel algorithms and techniques. We propose ICE to be a part of an ecosystem consisting of the XMT architecture, the PRAM algorithmic model, and ICE itself, that together deliver on the twin goal of easy programming and efficient parallelization of irregular programs. The XMT architecture, developed at UMD, can exploit fine-grained parallelism in irregular programs. We built the ICE compiler which translates the ICE language into the multithreaded XMTC language; the significance of this is that multi-threading is a feature shared by practically all current scalable parallel programming languages. Our main result is perhaps surprising: The run-time was comparable to XMTC with a 0.48% average gain for ICE across all benchmarks. Also, as an indication of ease of programming, we observed a reduction in code size in 7 out of 11 benchmarks vs. -
University of Cape Town Declaration
The copyright of this thesis vests in the author. No quotation from it or information derived from it is to be published without full acknowledgementTown of the source. The thesis is to be used for private study or non- commercial research purposes only. Cape Published by the University ofof Cape Town (UCT) in terms of the non-exclusive license granted to UCT by the author. University Automated Gateware Discovery Using Open Firmware Shanly Rajan Supervisor: Prof. M.R. Inggs Co-supervisor: Dr M. Welz University of Cape Town Declaration I understand the meaning of plagiarism and declare that all work in the dissertation, save for that which is properly acknowledged, is my own. It is being submitted for the degree of Master of Science in Engineering in the University of Cape Town. It has not been submitted before for any degree or examination in any other university. Signature of Author . Cape Town South Africa May 12, 2013 University of Cape Town i Abstract This dissertation describes the design and implementation of a mechanism that automates gateware1 device detection for reconfigurable hardware. The research facilitates the pro- cess of identifying and operating on gateware images by extending the existing infrastruc- ture of probing devices in traditional software by using the chosen technology. An automated gateware detection mechanism was devised in an effort to build a software system with the goal to improve performance and reduce software development time spent on operating gateware pieces by reusing existing device drivers in the framework of the chosen technology. This dissertation first investigates the system design to see how each of the user specifica- tions set for the KAT (Karoo Array Telescope) project in [28] could be achieved in terms of design decisions, toolchain selection and software modifications. -
Instructor's Manual
Instructor’s Manual Vol. 2: Presentation Material CCC Mesh/Torus Butterfly !*#? Sea Sick Hypercube Pyramid Behrooz Parhami This instructor’s manual is for Introduction to Parallel Processing: Algorithms and Architectures, by Behrooz Parhami, Plenum Series in Computer Science (ISBN 0-306-45970-1, QA76.58.P3798) 1999 Plenum Press, New York (http://www.plenum.com) All rights reserved for the author. No part of this instructor’s manual may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission. Contact the author at: ECE Dept., Univ. of California, Santa Barbara, CA 93106-9560, USA ([email protected]) Introduction to Parallel Processing: Algorithms and Architectures Instructor’s Manual, Vol. 2 (4/00), Page iv Preface to the Instructor’s Manual This instructor’s manual consists of two volumes. Volume 1 presents solutions to selected problems and includes additional problems (many with solutions) that did not make the cut for inclusion in the text Introduction to Parallel Processing: Algorithms and Architectures (Plenum Press, 1999) or that were designed after the book went to print. It also contains corrections and additions to the text, as well as other teaching aids. The spring 2000 edition of Volume 1 consists of the following parts (the next edition is planned for spring 2001): Vol. 1: Problem Solutions Part I Selected Solutions and Additional Problems Part II Question Bank, Assignments, and Projects Part III Additions, Corrections, and Other Updates Part IV Sample Course Outline, Calendar, and Forms Volume 2 contains enlarged versions of the figures and tables in the text, in a format suitable for use as transparency masters. -
Linux Kernel and Driver Development Training Slides
Linux Kernel and Driver Development Training Linux Kernel and Driver Development Training © Copyright 2004-2021, Bootlin. Creative Commons BY-SA 3.0 license. Latest update: October 9, 2021. Document updates and sources: https://bootlin.com/doc/training/linux-kernel Corrections, suggestions, contributions and translations are welcome! embedded Linux and kernel engineering Send them to [email protected] - Kernel, drivers and embedded Linux - Development, consulting, training and support - https://bootlin.com 1/470 Rights to copy © Copyright 2004-2021, Bootlin License: Creative Commons Attribution - Share Alike 3.0 https://creativecommons.org/licenses/by-sa/3.0/legalcode You are free: I to copy, distribute, display, and perform the work I to make derivative works I to make commercial use of the work Under the following conditions: I Attribution. You must give the original author credit. I Share Alike. If you alter, transform, or build upon this work, you may distribute the resulting work only under a license identical to this one. I For any reuse or distribution, you must make clear to others the license terms of this work. I Any of these conditions can be waived if you get permission from the copyright holder. Your fair use and other rights are in no way affected by the above. Document sources: https://github.com/bootlin/training-materials/ - Kernel, drivers and embedded Linux - Development, consulting, training and support - https://bootlin.com 2/470 Hyperlinks in the document There are many hyperlinks in the document I Regular hyperlinks: https://kernel.org/ I Kernel documentation links: dev-tools/kasan I Links to kernel source files and directories: drivers/input/ include/linux/fb.h I Links to the declarations, definitions and instances of kernel symbols (functions, types, data, structures): platform_get_irq() GFP_KERNEL struct file_operations - Kernel, drivers and embedded Linux - Development, consulting, training and support - https://bootlin.com 3/470 Company at a glance I Engineering company created in 2004, named ”Free Electrons” until Feb. -
Lawrence Berkeley National Laboratory Recent Work
Lawrence Berkeley National Laboratory Recent Work Title Parallel algorithms for finding connected components using linear algebra Permalink https://escholarship.org/uc/item/8ms106vm Authors Zhang, Y Azad, A Buluç, A Publication Date 2020-10-01 DOI 10.1016/j.jpdc.2020.04.009 Peer reviewed eScholarship.org Powered by the California Digital Library University of California Parallel Algorithms for Finding Connected Components using Linear Algebra Yongzhe Zhanga, Ariful Azadb, Aydın Buluc¸c aDepartment of Informatics, The Graduate University for Advanced Studies, SOKENDAI, Japan bDepartment of Intelligent Systems Engineering, Indiana University, Bloomington, IN, USA cComputational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA Abstract Finding connected components is one of the most widely used operations on a graph. Optimal serial algorithms for the problem have been known for half a century, and many competing parallel algorithms have been proposed over the last several decades under various different models of parallel computation. This paper presents a class of parallel connected-component algorithms designed using linear-algebraic primitives. These algorithms are based on a PRAM algorithm by Shiloach and Vishkin and can be designed using standard GraphBLAS operations. We demonstrate two algorithms of this class, one named LACC for Linear Algebraic Connected Components, and the other named FastSV which can be regarded as LACC’s simplification. With the support of the highly-scalable Combinatorial BLAS library, LACC and FastSV outperform the previous state-of-the-art algorithm by a factor of up to 12x for small to medium scale graphs. For large graphs with more than 50B edges, LACC and FastSV scale to 4K nodes (262K cores) of a Cray XC40 supercomputer and outperform previous algorithms by a significant margin. -
Quick Sort Algorithm Song Qin Dept
Quick Sort Algorithm Song Qin Dept. of Computer Sciences Florida Institute of Technology Melbourne, FL 32901 ABSTRACT each iteration. Repeat this on the rest of the unsorted region Given an array with n elements, we want to rearrange them in without the first element. ascending order. In this paper, we introduce Quick Sort, a Bubble sort works as follows: keep passing through the list, divide-and-conquer algorithm to sort an N element array. We exchanging adjacent element, if the list is out of order; when no evaluate the O(NlogN) time complexity in best case and O(N2) exchanges are required on some pass, the list is sorted. in worst case theoretically. We also introduce a way to approach the best case. Merge sort [4] has a O(NlogN) time complexity. It divides the 1. INTRODUCTION array into two subarrays each with N/2 items. Conquer each Search engine relies on sorting algorithm very much. When you subarray by sorting it. Unless the array is sufficiently small(one search some key word online, the feedback information is element left), use recursion to do this. Combine the solutions to brought to you sorted by the importance of the web page. the subarrays by merging them into single sorted array. 2 Bubble, Selection and Insertion Sort, they all have an O(N2) time In Bubble sort, Selection sort and Insertion sort, the O(N ) time complexity that limits its usefulness to small number of element complexity limits the performance when N gets very big. no more than a few thousand data points. -
Implementing the Map ADT Outline
Implementing the Map ADT Outline ´ The Map ADT ´ Implementation with Java Generics ´ A Hash Function ´ translation of a string key into an integer ´ Consider a few strategies for implementing a hash table ´ linear probing ´ quadratic probing ´ separate chaining hashing ´ OrderedMap using a binary search tree The Map ADT ´A Map models a searchable collection of key-value mappings ´A key is said to be “mapped” to a value ´Also known as: dictionary, associative array ´Main operations: insert, find, and delete Applications ´ Store large collections with fast operations ´ For a long time, Java only had Vector (think ArrayList), Stack, and Hashmap (now there are about 67) ´ Support certain algorithms ´ for example, probabilistic text generation in 127B ´ Store certain associations in meaningful ways ´ For example, to store connected rooms in Hunt the Wumpus in 335 The Map ADT ´A value is "mapped" to a unique key ´Need a key and a value to insert new mappings ´Only need the key to find mappings ´Only need the key to remove mappings 5 Key and Value ´With Java generics, you need to specify ´ the type of key ´ the type of value ´Here the key type is String and the value type is BankAccount Map<String, BankAccount> accounts = new HashMap<String, BankAccount>(); 6 put(key, value) get(key) ´Add new mappings (a key mapped to a value): Map<String, BankAccount> accounts = new TreeMap<String, BankAccount>(); accounts.put("M",); accounts.put("G", new BankAcnew BankAccount("Michel", 111.11)count("Georgie", 222.22)); accounts.put("R", new BankAccount("Daniel",