Data Structures and Algorithms for Data-Parallel Computing in a Managed Runtime
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Advanced Data Structures
Advanced Data Structures PETER BRASS City College of New York CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521880374 © Peter Brass 2008 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2008 ISBN-13 978-0-511-43685-7 eBook (EBL) ISBN-13 978-0-521-88037-4 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface page xi 1 Elementary Structures 1 1.1 Stack 1 1.2 Queue 8 1.3 Double-Ended Queue 16 1.4 Dynamical Allocation of Nodes 16 1.5 Shadow Copies of Array-Based Structures 18 2 Search Trees 23 2.1 Two Models of Search Trees 23 2.2 General Properties and Transformations 26 2.3 Height of a Search Tree 29 2.4 Basic Find, Insert, and Delete 31 2.5ReturningfromLeaftoRoot35 2.6 Dealing with Nonunique Keys 37 2.7 Queries for the Keys in an Interval 38 2.8 Building Optimal Search Trees 40 2.9 Converting Trees into Lists 47 2.10 -
Search Trees
Lecture III Page 1 “Trees are the earth’s endless effort to speak to the listening heaven.” – Rabindranath Tagore, Fireflies, 1928 Alice was walking beside the White Knight in Looking Glass Land. ”You are sad.” the Knight said in an anxious tone: ”let me sing you a song to comfort you.” ”Is it very long?” Alice asked, for she had heard a good deal of poetry that day. ”It’s long.” said the Knight, ”but it’s very, very beautiful. Everybody that hears me sing it - either it brings tears to their eyes, or else -” ”Or else what?” said Alice, for the Knight had made a sudden pause. ”Or else it doesn’t, you know. The name of the song is called ’Haddocks’ Eyes.’” ”Oh, that’s the name of the song, is it?” Alice said, trying to feel interested. ”No, you don’t understand,” the Knight said, looking a little vexed. ”That’s what the name is called. The name really is ’The Aged, Aged Man.’” ”Then I ought to have said ’That’s what the song is called’?” Alice corrected herself. ”No you oughtn’t: that’s another thing. The song is called ’Ways and Means’ but that’s only what it’s called, you know!” ”Well, what is the song then?” said Alice, who was by this time completely bewildered. ”I was coming to that,” the Knight said. ”The song really is ’A-sitting On a Gate’: and the tune’s my own invention.” So saying, he stopped his horse and let the reins fall on its neck: then slowly beating time with one hand, and with a faint smile lighting up his gentle, foolish face, he began.. -
The Random Access Zipper: Simple, Purely-Functional Sequences
The Random Access Zipper: Simple, Purely-Functional Sequences Kyle Headley and Matthew A. Hammer University of Colorado Boulder [email protected], [email protected] Abstract. We introduce the Random Access Zipper (RAZ), a simple, purely-functional data structure for editable sequences. The RAZ com- bines the structure of a zipper with that of a tree: like a zipper, edits at the cursor require constant time; by leveraging tree structure, relocating the edit cursor in the sequence requires log time. While existing data structures provide these time bounds, none do so with the same simplic- ity and brevity of code as the RAZ. The simplicity of the RAZ provides the opportunity for more programmers to extend the structure to their own needs, and we provide some suggestions for how to do so. 1 Introduction The singly-linked list is the most common representation of sequences for func- tional programmers. This structure is considered a core primitive in every func- tional language, and morever, the principles of its simple design recur througout user-defined structures that are \sequence-like". Though simple and ubiquitous, the functional list has a serious shortcoming: users may only efficiently access and edit the head of the list. In particular, random accesses (or edits) generally require linear time. To overcome this problem, researchers have developed other data structures representing (functional) sequences, most notably, finger trees [8]. These struc- tures perform well, allowing edits in (amortized) constant time and moving the edit location in logarithmic time. More recently, researchers have proposed the RRB-Vector [14], offering a balanced tree representation for immutable vec- tors. -
Design of Data Structures for Mergeable Trees∗
Design of Data Structures for Mergeable Trees∗ Loukas Georgiadis1; 2 Robert E. Tarjan1; 3 Renato F. Werneck1 Abstract delete(v): Delete leaf v from the forest. • Motivated by an application in computational topology, merge(v; w): Given nodes v and w, let P be the path we consider a novel variant of the problem of efficiently • from v to the root of its tree, and let Q be the path maintaining dynamic rooted trees. This variant allows an from w to the root of its tree. Restructure the tree operation that merges two tree paths. In contrast to the or trees containing v and w by merging the paths P standard problem, in which only one tree arc at a time and Q in a way that preserves the heap order. The changes, a single merge operation can change many arcs. merge order is unique if all node labels are distinct, In spite of this, we develop a data structure that supports which we can assume without loss of generality: if 2 merges and all other standard tree operations in O(log n) necessary, we can break ties by node identifier. See amortized time on an n-node forest. For the special case Figure 1. that occurs in the motivating application, in which arbitrary arc deletions are not allowed, we give a data structure with 1 an O(log n) amortized time bound per operation, which is merge(6,11) asymptotically optimal. The analysis of both algorithms is 3 2 not straightforward and requires ideas not previously used in 6 7 4 5 the study of dynamic trees. -
Bulk Updates and Cache Sensitivity in Search Trees
BULK UPDATES AND CACHE SENSITIVITY INSEARCHTREES TKK Research Reports in Computer Science and Engineering A Espoo 2009 TKK-CSE-A2/09 BULK UPDATES AND CACHE SENSITIVITY INSEARCHTREES Doctoral Dissertation Riku Saikkonen Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Faculty of Information and Natural Sciences, Helsinki University of Technology for public examination and debate in Auditorium T2 at Helsinki University of Technology (Espoo, Finland) on the 4th of September, 2009, at 12 noon. Helsinki University of Technology Faculty of Information and Natural Sciences Department of Computer Science and Engineering Teknillinen korkeakoulu Informaatio- ja luonnontieteiden tiedekunta Tietotekniikan laitos Distribution: Helsinki University of Technology Faculty of Information and Natural Sciences Department of Computer Science and Engineering P.O. Box 5400 FI-02015 TKK FINLAND URL: http://www.cse.tkk.fi/ Tel. +358 9 451 3228 Fax. +358 9 451 3293 E-mail: [email protected].fi °c 2009 Riku Saikkonen Layout: Riku Saikkonen (except cover) Cover image: Riku Saikkonen Set in the Computer Modern typeface family designed by Donald E. Knuth. ISBN 978-952-248-037-8 ISBN 978-952-248-038-5 (PDF) ISSN 1797-6928 ISSN 1797-6936 (PDF) URL: http://lib.tkk.fi/Diss/2009/isbn9789522480385/ Multiprint Oy Espoo 2009 AB ABSTRACT OF DOCTORAL DISSERTATION HELSINKI UNIVERSITY OF TECHNOLOGY P.O. Box 1000, FI-02015 TKK http://www.tkk.fi/ Author Riku Saikkonen Name of the dissertation Bulk Updates and Cache Sensitivity in Search Trees Manuscript submitted 09.04.2009 Manuscript revised 15.08.2009 Date of the defence 04.09.2009 £ Monograph ¤ Article dissertation (summary + original articles) Faculty Faculty of Information and Natural Sciences Department Department of Computer Science and Engineering Field of research Software Systems Opponent(s) Prof. -
Biased Finger Trees and Three-Dimensional Layers of Maxima
Purdue University Purdue e-Pubs Department of Computer Science Technical Reports Department of Computer Science 1993 Biased Finger Trees and Three-Dimensional Layers of Maxima Mikhail J. Atallah Purdue University, [email protected] Michael T. Goodrich Kumar Ramaiyer Report Number: 93-035 Atallah, Mikhail J.; Goodrich, Michael T.; and Ramaiyer, Kumar, "Biased Finger Trees and Three- Dimensional Layers of Maxima" (1993). Department of Computer Science Technical Reports. Paper 1052. https://docs.lib.purdue.edu/cstech/1052 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. HlASED FINGER TREES AND THREE-DIMENSIONAL LAYERS OF MAXIMA Mikhnil J. Atallah Michael T. Goodrich Kumar Ramaiyer eSD TR-9J-035 June 1993 (Revised 3/94) (Revised 4/94) Biased Finger Trees and Three-Dimensional Layers of Maxima Mikhail J. Atallah" Michael T. Goodricht Kumar Ramaiyert Dept. of Computer Sciences Dept. of Computer Science Dept. of Computer Science Purdue University Johns Hopkins University Johns Hopkins University W. Lafayette, IN 47907-1398 Baltimore, MD 21218-2694 Baltimore, MD 21218-2694 mjalDcs.purdue.edu goodrich~cs.jhu.edu kumarlDcs . j hu. edu Abstract We present a. method for maintaining biased search trees so as to support fast finger updates (i.e., updates in which one is given a pointer to the part of the hee being changed). We illustrate the power of such biased finger trees by showing how they can be used to derive an optimal O(n log n) algorithm for the 3-dimcnsionallayers-of-maxima problem and also obtain an improved method for dynamic point location. -
December, 1990
DIMACS Technical Report 90-75 December, 1990 FULLY PERSISTENT LISTS WITH CATENATION James R. Driscolll Department of Mathematics and Computer Science Dartmouth College Hanover, New Hampshire 03755 Daniel D. K. Sleator2 3 School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 Robert E. Tarjan4 5 Computer Science Department Princeton University Princeton, New Jersey 08544 and NEC Research Institute Princeton, New Jersey 08540 1 Supported in part by the NSF grant CCR-8809573, and by DARPA as monitored by the AFOSR grant AFOSR-904292 2 Supported in part by DIMACS 3 Supported in part by the NSF grant CCR-8658139 4 Permanent member of DIMACS 6 Supported in part by the Office of Naval Research contract N00014-87-K-0467 DIMACS is a cooperative project of Rutgers University, Princeton University, AT&T Bell Laboratories and Bellcore. DIMACS is an NSF Science and Technology Center, funded under contract STC-88-09648; and also receives support from the New Jersey Commission on Science and Technology. 1. Introduction In this paper we consider the problem of efficiently implementing a set of side-effect-free procedures for manipulating lists. These procedures are: makelist( d).- Create and return a new list of length 1 whose first and only element is d. first( X ) : Return the first element of list X. Pop(x): Return a new list that is the same as list X with its first element deleted. This operation does not effect X. catenate(X,Y): Return a new list that is the result of catenating list X and list Y, with X first, followed by Y (X and Y may be the same list). -
CS302ES Regulations
DATA STRUCTURES Subject Code: CS302ES Regulations : R18 - JNTUH Class: II Year B.Tech CSE I Semester Department of Computer Science and Engineering Bharat Institute of Engineering and Technology Ibrahimpatnam-501510,Hyderabad DATA STRUCTURES [CS302ES] COURSE PLANNER I. CourseOverview: This course introduces the core principles and techniques for Data structures. Students will gain experience in how to keep a data in an ordered fashion in the computer. Students can improve their programming skills using Data Structures Concepts through C. II. Prerequisite: A course on “Programming for Problem Solving”. III. CourseObjective: S. No Objective 1 Exploring basic data structures such as stacks and queues. 2 Introduces a variety of data structures such as hash tables, search trees, tries, heaps, graphs 3 Introduces sorting and pattern matching algorithms IV. CourseOutcome: Knowledge Course CO. Course Outcomes (CO) Level No. (Blooms Level) CO1 Ability to select the data structures that efficiently L4:Analysis model the information in a problem. CO2 Ability to assess efficiency trade-offs among different data structure implementations or L4:Analysis combinations. L5: Synthesis CO3 Implement and know the application of algorithms for sorting and pattern matching. Data Structures Data Design programs using a variety of data structures, CO4 including hash tables, binary and general tree L6:Create structures, search trees, tries, heaps, graphs, and AVL-trees. V. How program outcomes areassessed: Program Outcomes (PO) Level Proficiency assessed by PO1 Engineeering knowledge: Apply the knowledge of 2.5 Assignments, Mathematics, science, engineering fundamentals and Tutorials, Mock an engineering specialization to the solution of II B Tech I SEM CSE Page 45 complex engineering problems. -
Haskell Communities and Activities Report
Haskell Communities and Activities Report http://tinyurl.com/haskcar Thirty Fourth Edition — May 2018 Mihai Maruseac (ed.) Chris Allen Christopher Anand Moritz Angermann Francesco Ariis Heinrich Apfelmus Gershom Bazerman Doug Beardsley Jost Berthold Ingo Blechschmidt Sasa Bogicevic Emanuel Borsboom Jan Bracker Jeroen Bransen Joachim Breitner Rudy Braquehais Björn Buckwalter Erik de Castro Lopo Manuel M. T. Chakravarty Eitan Chatav Olaf Chitil Alberto Gómez Corona Nils Dallmeyer Tobias Dammers Kei Davis Dimitri DeFigueiredo Richard Eisenberg Maarten Faddegon Dennis Felsing Olle Fredriksson Phil Freeman Marc Fontaine PÁLI Gábor János Michał J. Gajda Ben Gamari Michael Georgoulopoulos Andrew Gill Mikhail Glushenkov Mark Grebe Gabor Greif Adam Gundry Jennifer Hackett Jurriaan Hage Martin Handley Bastiaan Heeren Sylvain Henry Joey Hess Kei Hibino Guillaume Hoffmann Graham Hutton Nicu Ionita Judah Jacobson Patrik Jansson Wanqiang Jiang Dzianis Kabanau Nikos Karagiannidis Anton Kholomiov Oleg Kiselyov Ivan Krišto Yasuaki Kudo Harendra Kumar Rob Leslie David Lettier Ben Lippmeier Andres Löh Rita Loogen Tim Matthews Simon Michael Andrey Mokhov Dino Morelli Damian Nadales Henrik Nilsson Wisnu Adi Nurcahyo Ulf Norell Ivan Perez Jens Petersen Sibi Prabakaran Bryan Richter Herbert Valerio Riedel Alexey Radkov Vaibhav Sagar Kareem Salah Michael Schröder Christian Höner zu Siederdissen Ben Sima Jeremy Singer Gideon Sireling Erik Sjöström Chris Smith Michael Snoyman David Sorokin Lennart Spitzner Yuriy Syrovetskiy Jonathan Thaler Henk-Jan van Tuyl Tillmann Vogt Michael Walker Li-yao Xia Kazu Yamamoto Yuji Yamamoto Brent Yorgey Christina Zeller Marco Zocca Preface This is the 34th edition of the Haskell Communities and Activities Report. This report has 148 entries, 5 more than in the previous edition. -
Concurrent Tries with Efficient Non-Blocking Snapshots
Concurrent Tries with Efficient Non-Blocking Snapshots Aleksandar Prokopec Nathan G. Bronson Phil Bagwell Martin Odersky EPFL Stanford Typesafe EPFL aleksandar.prokopec@epfl.ch [email protected] [email protected] martin.odersky@epfl.ch Abstract root T1: CAS root We describe a non-blocking concurrent hash trie based on shared- C3 T2: CAS C3 memory single-word compare-and-swap instructions. The hash trie supports standard mutable lock-free operations such as insertion, C2 ··· C2 C2’ ··· removal, lookup and their conditional variants. To ensure space- efficiency, removal operations compress the trie when necessary. C1 k3 C1’ k3 C1 k3 k5 We show how to implement an efficient lock-free snapshot op- k k k k k k k eration for concurrent hash tries. The snapshot operation uses a A 1 2 B 1 2 4 1 2 single-word compare-and-swap and avoids copying the data struc- ture eagerly. Snapshots are used to implement consistent iterators Figure 1. Hash tries and a linearizable size retrieval. We compare concurrent hash trie performance with other concurrent data structures and evaluate the performance of the snapshot operation. 2. We introduce a non-blocking, atomic constant-time snapshot Categories and Subject Descriptors E.1 [Data structures]: Trees operation. We show how to use them to implement atomic size retrieval, consistent iterators and an atomic clear operation. General Terms Algorithms 3. We present benchmarks that compare performance of concur- Keywords hash trie, concurrent data structure, snapshot, non- rent tries against other concurrent data structures across differ- blocking ent architectures. 1. Introduction Section 2 illustrates usefulness of snapshots. -
A Contention Adapting Approach to Concurrent Ordered Sets$
A Contention Adapting Approach to Concurrent Ordered SetsI Konstantinos Sagonasa,b, Kjell Winblada,∗ aDepartment of Information Technology, Uppsala University, Sweden bSchool of Electrical and Computer Engineering, National Technical University of Athens, Greece Abstract With multicores being ubiquitous, concurrent data structures are increasingly important. This article proposes a novel approach to concurrent data structure design where the data structure dynamically adapts its synchronization granularity based on the detected contention and the amount of data that operations are accessing. This approach not only has the potential to reduce overheads associated with synchronization in uncontended scenarios, but can also be beneficial when the amount of data that operations are accessing atomically is unknown. Using this adaptive approach we create a contention adapting search tree (CA tree) that can be used to implement concurrent ordered sets and maps with support for range queries and bulk operations. We provide detailed proof sketches for the linearizability as well as deadlock and livelock freedom of CA tree operations. We experimentally compare CA trees to state-of-the-art concurrent data structures and show that CA trees beat the best of the data structures that we compare against by over 50% in scenarios that contain basic set operations and range queries, outperform them by more than 1200% in scenarios that also contain range updates, and offer performance and scalability that is better than many of them on workloads that only contain basic set operations. Keywords: concurrent data structures, ordered sets, linearizability, range queries 1. Introduction With multicores being widespread, the need for efficient concurrent data structures has increased. -
Handout 09: Suggested Project Topics
CS166 Handout 09 Spring 2021 April 13, 2021 Suggested Project Topics Here is a list of data structures and families of data structures we think you might find interesting topics for your research project. You're by no means limited to what's contained here; if you have another data structure you'd like to explore, feel free to do so! My Wish List Below is a list of topics where, each quarter, I secretly think “I hope someone wants to pick this topic this quarter!” These are data structures I’ve always wanted to learn a bit more about or that I think would be particularly fun to do a deep dive into. You are not in any way, shape, or form required to pick something from this list, and we aren’t offer- ing extra credit or anything like that if you do choose to select one of these topics. However, if any of them seem interesting to you, we’d be excited to see what you come up with over the quarter. • Bentley-Saxe dynamization (turning static data structures into dynamic data structures) • Bε-trees (a B-tree variant designed to minimize writes) • Chazelle and Guibas’s O(log n + k) 3D range search (fast range searches in 3D) • Crazy good chocolate pop tarts (deamortizing binary search trees) • Durocher’s RMQ structure (fast RMQ without the Method of Four Russians) • Dynamic prefix sum lower bounds (proving lower bounds on dynamic prefix parity) • Farach’s suffix tree algorithm (a brilliant, beautiful divide-and-conquer algorithm) • Geometric greedy trees (lower bounds on BSTs giving rise to a specific BST) • Ham sandwich trees (fast searches