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Trans-Dichotomous Algorithms for Minimum Spanning Trees and Shortest Paths
JOURNAL or COMPUTER AND SYSTEM SCIENCES 48, 533-551 (1994) Trans-dichotomous Algorithms for Minimum Spanning Trees and Shortest Paths MICHAEL L. FREDMAN* University of California at San Diego, La Jolla, California 92093, and Rutgers University, New Brunswick, New Jersey 08903 AND DAN E. WILLARDt SUNY at Albany, Albany, New York 12203 Received February 5, 1991; revised October 20, 1992 Two algorithms are presented: a linear time algorithm for the minimum spanning tree problem and an O(m + n log n/log log n) implementation of Dijkstra's shortest-path algorithm for a graph with n vertices and m edges. The second algorithm surpasses information theoretic limitations applicable to comparison-based algorithms. Both algorithms utilize new data structures that extend the fusion tree method. © 1994 Academic Press, Inc. 1. INTRODUCTION We extend the fusion tree method [7J to develop a linear-time algorithm for the minimum spanning tree problem and an O(m + n log n/log log n) implementation of Dijkstra's shortest-path algorithm for a graph with n vertices and m edges. The implementation of Dijkstra's algorithm surpasses information theoretic limitations applicable to comparison-based algorithms. Our extension of the fusion tree method involves the development of a new data structure, the atomic heap. The atomic heap accommodates heap (priority queue) operations in constant amortized time under suitable polylog restrictions on the heap size. Our linear-time minimum spanning tree algorithm results from a direct application of the atomic heap. To obtain the shortest-path algorithm, we first use the atomic heat as a building block to construct a new data structure, the AF-heap, which has no explicit size restric- tion and surpasses information theoretic limitations applicable to comparison-based algorithms. -
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. -
Fast As a Shadow, Expressive As a Tree: Hybrid Memory Monitoring for C
Fast as a Shadow, Expressive as a Tree: Hybrid Memory Monitoring for C Nikolai Kosmatov1 with Arvid Jakobsson2, Guillaume Petiot1 and Julien Signoles1 [email protected] [email protected] SASEFOR, November 24, 2015 A.Jakobsson, N.Kosmatov, J.Signoles (CEA) Hybrid Memory Monitoring for C 2015-11-24 1 / 48 Outline Context and motivation Frama-C, a platform for analysis of C code Motivation The memory monitoring library An overview Patricia trie model Shadow memory based model The Hybrid model Design principles Illustrating example Dataflow analysis An overview How it proceeds Evaluation Conclusion and future work A.Jakobsson, N.Kosmatov, J.Signoles (CEA) Hybrid Memory Monitoring for C 2015-11-24 2 / 48 Context and motivation Frama-C, a platform for analysis of C code Outline Context and motivation Frama-C, a platform for analysis of C code Motivation The memory monitoring library An overview Patricia trie model Shadow memory based model The Hybrid model Design principles Illustrating example Dataflow analysis An overview How it proceeds Evaluation Conclusion and future work A.Jakobsson, N.Kosmatov, J.Signoles (CEA) Hybrid Memory Monitoring for C 2015-11-24 3 / 48 Context and motivation Frama-C, a platform for analysis of C code A brief history I 90's: CAVEAT, Hoare logic-based tool for C code at CEA I 2000's: CAVEAT used by Airbus during certification process of the A380 (DO-178 level A qualification) I 2002: Why and its C front-end Caduceus (at INRIA) I 2006: Joint project on a successor to CAVEAT and Caduceus I 2008: First public release of Frama-C (Hydrogen) I Today: Frama-C Sodium (v.11) I Multiple projects around the platform I A growing community of users. -
Rockjit: Securing Just-In-Time Compilation Using Modular Control-Flow Integrity
RockJIT: Securing Just-In-Time Compilation Using Modular Control-Flow Integrity Ben Niu Gang Tan Lehigh University Lehigh University 19 Memorial Dr West 19 Memorial Dr West Bethlehem, PA, 18015 Bethlehem, PA, 18015 [email protected] [email protected] ABSTRACT For performance, modern managed language implementations Managed languages such as JavaScript are popular. For perfor- adopt Just-In-Time (JIT) compilation. Instead of performing pure mance, modern implementations of managed languages adopt Just- interpretation, a JIT compiler dynamically compiles programs into In-Time (JIT) compilation. The danger to a JIT compiler is that an native code and performs optimization on the fly based on informa- attacker can often control the input program and use it to trigger a tion collected through runtime profiling. JIT compilation in man- vulnerability in the JIT compiler to launch code injection or JIT aged languages is the key to high performance, which is often the spraying attacks. In this paper, we propose a general approach only metric when comparing JIT engines, as seen in the case of called RockJIT to securing JIT compilers through Control-Flow JavaScript. Hereafter, we use the term JITted code for native code Integrity (CFI). RockJIT builds a fine-grained control-flow graph that is dynamically generated by a JIT compiler, and code heap for from the source code of the JIT compiler and dynamically up- memory pages that hold JITted code. dates the control-flow policy when new code is generated on the fly. In terms of security, JIT brings its own set of challenges. First, a Through evaluation on Google’s V8 JavaScript engine, we demon- JIT compiler is large and usually written in C/C++, which lacks strate that RockJIT can enforce strong security on a JIT compiler, memory safety. -
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. -
Speculative Separation for Privatization and Reductions
Speculative Separation for Privatization and Reductions Nick P. Johnson Hanjun Kim Prakash Prabhu Ayal Zaksy David I. August Princeton University, Princeton, NJ yIntel Corporation, Haifa, Israel fnpjohnso, hanjunk, pprabhu, [email protected] [email protected] Abstract Memory Layout Static Speculative Automatic parallelization is a promising strategy to improve appli- Speculative LRPD [22] R−LRPD [7] cation performance in the multicore era. However, common pro- Privateer (this work) gramming practices such as the reuse of data structures introduce Dynamic PD [21] artificial constraints that obstruct automatic parallelization. Privati- Polaris [29] ASSA [14] zation relieves these constraints by replicating data structures, thus Static Array Expansion [10] enabling scalable parallelization. Prior privatization schemes are Criterion DSA [31] RSSA [23] limited to arrays and scalar variables because they are sensitive to Privatization Manual Paralax [32] STMs [8, 18] the layout of dynamic data structures. This work presents Privateer, the first fully automatic privatization system to handle dynamic and Figure 1: Privatization Criterion and Memory Layout. recursive data structures, even in languages with unrestricted point- ers. To reduce sensitivity to memory layout, Privateer speculatively separates memory objects. Privateer’s lightweight runtime system contention and relaxes the program dependence structure by repli- validates speculative separation and speculative privatization to en- cating the reused storage locations, producing multiple copies in sure correct parallel execution. Privateer enables automatic paral- memory that support independent, concurrent access. Similarly, re- lelization of general-purpose C/C++ applications, yielding a ge- duction techniques relax ordering constraints on associative, com- omean whole-program speedup of 11.4× over best sequential ex- mutative operators by replacing (or expanding) storage locations. -
Lecture 1 — 24 January 2017 1 Overview 2 Administrivia 3 The
CS 224: Advanced Algorithms Spring 2017 Lecture 1 | 24 January 2017 Prof. Jelani Nelson Scribe: Jerry Ma 1 Overview We introduce the word RAM model of computation, which features fixed-size storage blocks (\words") similar to modern integer data types. We also introduce the predecessor problem and demonstrate solutions to the problem that are faster than optimal comparison-based methods. 2 Administrivia • Personnel: Jelani Nelson (instructor) and Tom Morgan (TF) • Course site: people.seas.harvard.edu/~cs224 • Course staff email: [email protected] • Prerequisites: CS 124/125 and probability. • Coursework: lecture scribing, problem sets, and a final project. Students will also assist in grading problem sets. No coding. • Topics will include those from CS 124/125 at a deeper level of exposition, as well as entirely new topics. 3 The Predecessor Problem In the predecessor, we wish to maintain a ordered set S = fX1;X2; :::; Xng subject to the prede- cessor query: pred(z) = maxfx 2 Sjx < zg Usually, we do this by representing S in a data structure. In the static predecessor problem, S does not change between pred queries. In the dynamic predecessor problem, S may change through the operations: insert(z): S S [ fzg del(z): S S n fzg For the static predecessor problem, a good solution is to store S as a sorted array. pred can then be implemented via binary search. This requires Θ(n) space, Θ(log n) runtime for pred, and Θ(n log n) preprocessing time. 1 For the dynamic predecessor problem, we can maintain S in a balanced binary search tree, or BBST (e.g. -
Download/Repository/Ivan Fratric.Pdf, 2012
UC Irvine UC Irvine Electronic Theses and Dissertations Title Binary Recompilation via Dynamic Analysis and the Protection of Control and Data-flows Therein Permalink https://escholarship.org/uc/item/4gd0b9ht Author Nash, Joseph Michael Publication Date 2020 License https://creativecommons.org/licenses/by-sa/4.0/ 4.0 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA, IRVINE Binary Recompilation via Dynamic Analysis and the Protection of Control and Data-flows Therein DISSERTATION submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in Computer Science by Joseph Nash Dissertation Committee: Professor Michael Franz, Chair Professor Ardalan Amiri Sani Professor Alexander V. Veidenbaum 2020 Parts of Chapter3 c 2020 ACM Reprinted, with permission, from BinRec: Attack Surface Reduction Through Dynamic Binary Recovery., Anil Altinay, Joseph Nash, Taddeus Kroes, Prahbu Rajasekaran, Dixin Zhou, Adrian Dabrowski, David Gens, Yeoul Na, Stijn Volckaert, Herbert Bos, Cristiano Giuffrida, Michael Franz, in Proceedings of the Fifteenth EuroSys Conference , EUROSYS 2020. Parts of Chapter5 c 2018 Springer. Reprinted, with permission, from Hardware Assisted Randomization of Data, Brian Belleville, Hyungon Moon, Jangseop Shin, Dongil Hwang, Joseph M. Nash, Seonhwa Jung, Yeoul Na, Stijn Volckaert, Per Larsen, Yunheung Paek, Michael Franz , in Proceedings of the 21st International Symposium on Research in Attacks, Intrusions and Defenses, RAID 2018. Parts of Chapter4 c 2017 ACM. Reprinted, with permission, from Control-Flow Integrity: Precision, Security, and Performance, Nathan Burow, Scott A. Carr, Joseph Nash, Per Larsen, Michael Franz, Stefan Brunthaler, Mathias Payer. , in Proceedings of the 21st International Symposium on Research in Attacks, Intrusions and Defenses, ACM Computing Surveys 2017. -
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.