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Space-Efficient Data Structures, Streams, and Algorithms
Andrej Brodnik Alejandro López-Ortiz Venkatesh Raman Alfredo Viola (Eds.) Festschrift Space-Efficient Data Structures, Streams, LNCS 8066 and Algorithms Papers in Honor of J. Ian Munro on the Occasion of His 66th Birthday 123 Lecture Notes in Computer Science 8066 Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Alfred Kobsa University of California, Irvine, CA, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen TU Dortmund University, Germany Madhu Sudan Microsoft Research, Cambridge, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max Planck Institute for Informatics, Saarbruecken, Germany Andrej Brodnik Alejandro López-Ortiz Venkatesh Raman Alfredo Viola (Eds.) Space-Efficient Data Structures, Streams, and Algorithms Papers in Honor of J. Ian Munro on the Occasion of His 66th Birthday 13 Volume Editors Andrej Brodnik University of Ljubljana, Faculty of Computer and Information Science Ljubljana, Slovenia and University of Primorska, -
A Complete Bibliography of Publications in Nordisk Tidskrift for Informationsbehandling, BIT, and BIT Numerical Mathematics
A Complete Bibliography of Publications in Nordisk Tidskrift for Informationsbehandling, BIT,andBIT Numerical Mathematics Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 09 June 2021 Version 3.54 Title word cross-reference [3105, 328, 469, 655, 896, 524, 873, 455, 779, 946, 2944, 297, 1752, 670, 2582, 1409, 1987, 915, 808, 761, 916, 2071, 2198, 1449, 780, 959, 1105, 1021, 497, 2589]. A(α) #24873 [1089]. [896, 2594, 333]. A∗ [2013]. A∗Ax = b [2369]. n A [1640, 566, 947, 1580, 1460]. A = a2 +1 − 0 n (3) [2450]. (A λB) [1414]. 0=1 [1242]. 1 [334]. α [824, 1580]. AN [1622]. A(#) [3439]. − 12 [3037, 2711]. 1 2 [1097]. 1:0 [3043]. 10 AX − XB = C [2195, 2006]. [838]. 11 [1311]. 2 AXD − BXC = E [1101]. B [2144, 1953, 2291, 2162, 3047, 886, 2551, 957, [2187, 1575, 1267, 1409, 1489, 1991, 1191, 2007, 2552, 1832, 949, 3024, 3219, 2194]. 2; 3 979, 1819, 1597, 1823, 1773]. β [824]. BN n − p − − [1490]. 2 1 [320]. 2 1 [100]. 2m 4 [1181]. BS [1773]. BSI [1446]. C0 [2906]. C1 [1105]. 3 [2119, 1953, 2531, 1351, 2551, 1292, [3202]. C2 [3108, 2422, 3000, 2036]. χ2 1793, 949, 1356, 2711, 2227, 570]. [30, 31]. Cln(θ); (n ≥ 2) [2929]. cos [228]. D 3; 000; 000; 000 [575, 637]. -
Fundamental Data Structures Contents
Fundamental Data Structures Contents 1 Introduction 1 1.1 Abstract data type ........................................... 1 1.1.1 Examples ........................................... 1 1.1.2 Introduction .......................................... 2 1.1.3 Defining an abstract data type ................................. 2 1.1.4 Advantages of abstract data typing .............................. 4 1.1.5 Typical operations ...................................... 4 1.1.6 Examples ........................................... 5 1.1.7 Implementation ........................................ 5 1.1.8 See also ............................................ 6 1.1.9 Notes ............................................. 6 1.1.10 References .......................................... 6 1.1.11 Further ............................................ 7 1.1.12 External links ......................................... 7 1.2 Data structure ............................................. 7 1.2.1 Overview ........................................... 7 1.2.2 Examples ........................................... 7 1.2.3 Language support ....................................... 8 1.2.4 See also ............................................ 8 1.2.5 References .......................................... 8 1.2.6 Further reading ........................................ 8 1.2.7 External links ......................................... 9 1.3 Analysis of algorithms ......................................... 9 1.3.1 Cost models ......................................... 9 1.3.2 Run-time analysis -
*Dictionary Data Structures 3
CHAPTER *Dictionary Data Structures 3 The exploration efficiency of algorithms like A* is often measured with respect to the number of expanded/generated problem graph nodes, but the actual runtimes depend crucially on how the Open and Closed lists are implemented. In this chapter we look closer at efficient data structures to represent these sets. For the Open list, different options for implementing a priority queue data structure are consid- ered. We distinguish between integer and general edge costs, and introduce bucket and advanced heap implementations. For efficient duplicate detection and removal we also look at hash dictionaries. We devise a variety of hash functions that can be computed efficiently and that minimize the number of collisions by approximating uniformly distributed addresses, even if the set of chosen keys is not (which is almost always the case). Next we explore memory-saving dictionaries, the space requirements of which come close to the information-theoretic lower bound and provide a treatment of approximate dictionaries. Subset dictionaries address the problem of finding partial state vectors in a set. Searching the set is referred to as the Subset Query or the Containment Query problem. The two problems are equivalent to the Partial Match retrieval problem for retrieving a partially specified input query word from a file of k-letter words with k being fixed. A simple example is the search for a word in a crossword puzzle. In a state space search, subset dictionaries are important to store partial state vectors like dead-end patterns in Sokoban that generalize pruning rules (see Ch. -
Seeking for the Best Priority Queue: Lessons Learnt
Updated 20 October, 2013 Seeking for the best priority queue: Lessons learnt Jyrki Katajainen1; 2 Stefan Edelkamp3, Amr Elmasry4, Claus Jensen5 1 University of Copenhagen 4 Alexandria University 2 Jyrki Katajainen and Company 5 The Royal Library 3 University of Bremen These slides are available from my research information system (see http://www.diku.dk/~jyrki/ under Presentations). c Performance Engineering Laboratory Seminar 13391: Schloss Dagstuhl, Germany (1) Categorization of priority queues insert minimum input: locator input: none output: none output: locator Elementary delete extract-min minimum input: locator p minimum() insert output: none delete(p) extract-min Addressable delete decrease decrease input: locator, value Mergeable output: none union union input: two priority queues output: one priority queue c Performance Engineering Laboratory Seminar 13391: Schloss Dagstuhl, Germany (2) Structure of this talk: Research question What is the "best" priority queue? I: Elementary II: Addressable III: Mergeable c Performance Engineering Laboratory Seminar 13391: Schloss Dagstuhl, Germany (3) Binary heaps 0 minimum() 8 return a[0] 12 10 26 insert(x) 3 4 5 6 a[N] = x 75 46 7512 siftup(N) 7 N += 1 80 extract-min() N = 8 min = a[0] N −= 1 a 8 10 26 75 12 46 75 80 a[0] = a[N] 02341 675 siftdown(0) left-child(i) return min return 2i + 1 right-child(i) Elementary: array-based return 2i + 2 Addressable: pointer-based parent(i) Mergeable: forest of heaps return b(i − 1)=2c c Performance Engineering Laboratory Seminar 13391: Schloss Dagstuhl, Germany (4) Market analysis Efficiency binary binomial Fibonacci run-relaxed heap queue heap heap Operation [Wil64] [Vui78] [FT87] [DGST88] worst case worst case amortized worst case minimum Θ(1) Θ(1) Θ(1) Θ(1) insert Θ(lg N) Θ(1) Θ(1) Θ(1) decrease Θ(lg N) Θ(lg N) Θ(1) Θ(1) delete Θ(lg N) Θ(lg N) Θ(lg N) Θ(lg N) union Θ(lg M×lg N) Θ(minflg M; lg Ng) Θ(1) Θ(minflg M; lg Ng) Here M and N denote the number of elements in the priority queues just prior to the operation. -
An English-Persian Dictionary of Algorithms and Data Structures
An EnglishPersian Dictionary of Algorithms and Data Structures a a zarrabibasuacir ghodsisharifedu algorithm B A all pairs shortest path absolute p erformance guarantee b alphab et abstract data typ e alternating path accepting state alternating Turing machine d Ackermans function alternation d Ackermanns function amortized cost acyclic digraph amortized worst case acyclic directed graph ancestor d acyclic graph and adaptive heap sort ANSI b adaptivekdtree antichain adaptive sort antisymmetric addresscalculation sort approximation algorithm adjacencylist representation arc adjacencymatrix representation array array index adjacency list array merging adjacency matrix articulation p oint d adjacent articulation vertex d b admissible vertex assignmentproblem adversary asso ciation list algorithm asso ciative binary function asso ciative array binary GCD algorithm asymptotic b ound binary insertion sort asymptotic lower b ound binary priority queue asymptotic space complexity binary relation binary search asymptotic time complexity binary trie asymptotic upp er b ound c bingo sort asymptotically equal to bipartite graph asymptotically tightbound bipartite matching -
Lazy Search Trees
Lazy Search Trees Bryce Sandlund1 and Sebastian Wild2 1David R. Cheriton School of Computer Science, University of Waterloo 2Department of Computer Science, University of Liverpool October 20, 2020 Abstract We introduce the lazy search tree data structure. The lazy search tree is a comparison- based data structure on the pointer machine that supports order-based operations such as rank, select, membership, predecessor, successor, minimum, and maximum while providing dynamic operations insert, delete, change-key, split, and merge. We analyze the performance of our data structure based on a partition of current elements into a set of gaps {∆i} based on rank. A query falls into a particular gap and splits the gap into two new gaps at a rank r associated with the query operation. If we define B = ∑i S∆iS log2(n~S∆iS), our performance over a sequence of n insertions and q distinct queries is O(B + min(n log log n; n log q)). We show B is a lower bound. Effectively, we reduce the insertion time of binary search trees from Θ(log n) to O(min(log(n~S∆iS) + log log S∆iS; log q)), where ∆i is the gap in which the inserted element falls. Over a sequence of n insertions and q queries, a time bound of O(n log q + q log n) holds; better bounds are possible when queries are non-uniformly distributed. As an extreme case of non-uniformity, if all queries are for the minimum element, the lazy search tree performs as a priority queue with O(log log n) time insert and decrease-key operations. -
The Algorithms and Data Structures Course Multicomponent Complexity and Interdisciplinary Connections
Technium Vol. 2, Issue 5 pp.161-171 (2020) ISSN: 2668-778X www.techniumscience.com The Algorithms and Data Structures course multicomponent complexity and interdisciplinary connections Gregory Korotenko Dnipro University of Technology, Ukraine [email protected] Leonid Korotenko Dnipro University of Technology, Ukraine [email protected] Abstract. The experience of modern education shows that the trajectory of preparing students is extremely important for their further adaptation in the structure of widespread digitalization, digital transformations and the accumulation of experience with digital platforms of business and production. At the same time, there continue to be reports of a constant (catastrophic) lack of personnel in this area. The basis of the competencies of specialists in the field of computing is the ability to solve algorithmic problems that they have not been encountered before. Therefore, this paper proposes to consider the features of teaching the course Algorithms and Data Structures and possible ways to reduce the level of complexity in its study. Keywords. learning, algorithms, data structures, data processing, programming, mathematics, interdisciplinarity. 1. Introduction The analysis of electronic resources and literary sources allows for the conclusion that the Algorithms and Data Structures course is one of the cornerstones for the study programs related to computing. Moreover, this can be considered not only from the point of view of entering the profession, but also from the point of view of preparation for an interview in hiring as a programmer, including at a large IT organization (Google, Microsoft, Apple, Amazon, etc.) or for a promising startup [1]. As a rule, this course is characterized by an abundance of complex data structures and various algorithms for their processing. -
Weak Heaps and Friends Recent Developments Edelkamp, Stefan; Elmasry, Amr; Katajainen, Jyrki; Weiß, Armin
Weak heaps and friends recent developments Edelkamp, Stefan; Elmasry, Amr; Katajainen, Jyrki; Weiß, Armin Published in: Combinatorial Algorithms DOI: 10.1007/978-3-642-45278-9_1 Publication date: 2013 Document version Peer reviewed version Document license: Other Citation for published version (APA): Edelkamp, S., Elmasry, A., Katajainen, J., & Weiß, A. (2013). Weak heaps and friends: recent developments. In T. Lecroq, & L. Mouchard (Eds.), Combinatorial Algorithms: 24th International Workshop, IWOCA 2013, Rouen, France, July 10-12, 2013, Revised Selected Papers (pp. 1-6). Springer. Lecture notes in computer science Vol. 8288 https://doi.org/10.1007/978-3-642-45278-9_1 Download date: 30. sep.. 2021 Weak Heaps and Friends: Recent Developments Stefan Edelkamp1, Amr Elmasry2, Jyrki Katajainen3, and Armin Weiß4 1 Faculty 3|Mathematics and Computer Science, University of Bremen PO Box 330 440, 28334 Bremen, Germany 2 Department of Computer Engineering and Systems, Alexandria University Alexandria 21544, Egypt 3 Department of Computer Science, University of Copenhagen Universitetsparken 5, 2100 Copenhagen East, Denmark 4 Institute for Formal Methods in Computer Science, University of Stuttgart Universit¨atstraße 38, 70569 Stuttgart, Germany Abstract. A weak heap is a variant of a binary heap where, for each node, the heap ordering is enforced only for one of its two children. In 1993, Dutton showed that this data structure yields a simple worst- case-efficient sorting algorithm. In this paper we review the refinements proposed to the basic data structure that improve the efficiency even further. Ultimately, minimum and insert operations are supported in O(1) worst-case time and extract-min operation in O(lg n) worst-case time involving at most lg n + O(1) element comparisons. -
Lazy Search Trees §1 Introduction ⋅ 1
Lazy Search Trees Bryce Sandlund1 and Sebastian Wild2 1David R. Cheriton School of Computer Science, University of Waterloo 2Department of Computer Science, University of Liverpool October 20, 2020 Abstract We introduce the lazy search tree data structure. The lazy search tree is a comparison- based data structure on the pointer machine that supports order-based operations such as rank, select, membership, predecessor, successor, minimum, and maximum while providing dynamic operations insert, delete, change-key, split, and merge. We analyze the performance of our data structure based on a partition of current elements into a set of gaps {∆i} based on rank. A query falls into a particular gap and splits the gap into two new gaps at a rank r associated with the query operation. If we define B = ∑i S∆iS log2(n~S∆iS), our performance over a sequence of n insertions and q distinct queries is O(B + min(n log log n,n log q)). We show B is a lower bound. Effectively, we reduce the insertion time of binary search trees from Θ(log n) to O(min(log(n~S∆iS) + log log S∆iS, log q)), where ∆i is the gap in which the inserted element falls. Over a sequence of n insertions and q queries, a time bound of O(n log q + q log n) holds; better bounds are possible when queries are non-uniformly distributed. As an extreme case of non-uniformity, if all queries are for the minimum element, the lazy search tree performs as a priority queue with O(log log n) time insert and decrease-key operations. -
Weak Updates and Separation Logic
Weak updates and separation logic Gang Tan1, Zhong Shao2, Xinyu Feng3, and Hongxu Cai4 1Lehigh University, 2Yale University 3Toyota Technological Institute at Chicago, 4Google Inc. Abstract. Separation Logic (SL) provides a simple but powerful technique for reasoning about imperative programs that use shared data structures. Unfortu- nately, SL supports only “strong updates”, in which mutation to a heap location is safe only if a unique reference is owned. This limits the applicability of SL when reasoning about the interaction between many high-level languages (e.g., ML, Java, C#) and low-level ones since these high-level languages do not support strong updates. Instead, they adopt the discipline of “weak updates”, in which there is a global “heap type” to enforce the invariant of type-preserving heap up- dates. We present SLw, a logic that extends SL with reference types and elegantly reasons about the interaction between strong and weak updates. We also describe a semantic framework for reference types; this framework is used to prove the soundness of SLw. 1 Introduction Reasoning about mutable, aliased heap data structures is essential for proving properties or checking safety of imperative programs. Two distinct approaches perform such kind of reasoning: Separation Logic, and a type-based approach employed by many high- level programming languages. Extending Hoare Logic, the seminal work of Separation Logic (SL [10, 13]) is a powerful framework for proving properties of low-level imperative programs. Through its separating conjunction operator and frame rule, SL supports local reasoning about heap updates, storage allocation, and explicit storage deallocation. SL supports “strong updates”: as long as a unique reference to a heap cell is owned, the heap-update rule of SL allows the cell to be updated with any value: {(e 7→ −) ∗ p}[e] := e′{(e 7→ e′) ∗ p} (1) In the above heap-update rule, there is no restriction on the new value e′. -
Data Structures
KARNATAKA STATE OPEN UNIVERSITY DATA STRUCTURES BCA I SEMESTER SUBJECT CODE: BCA 04 SUBJECT TITLE: DATA STRUCTURES 1 STRUCTURE OF THE COURSE CONTENT BLOCK 1 PROBLEM SOLVING Unit 1: Top-down Design – Implementation Unit 2: Verification – Efficiency Unit 3: Analysis Unit 4: Sample Algorithm BLOCK 2 LISTS, STACKS AND QUEUES Unit 1: Abstract Data Type (ADT) Unit 2: List ADT Unit 3: Stack ADT Unit 4: Queue ADT BLOCK 3 TREES Unit 1: Binary Trees Unit 2: AVL Trees Unit 3: Tree Traversals and Hashing Unit 4: Simple implementations of Tree BLOCK 4 SORTING Unit 1: Insertion Sort Unit 2: Shell sort and Heap sort Unit 3: Merge sort and Quick sort Unit 4: External Sort BLOCK 5 GRAPHS Unit 1: Topological Sort Unit 2: Path Algorithms Unit 3: Prim‘s Algorithm Unit 4: Undirected Graphs – Bi-connectivity Books: 1. R. G. Dromey, ―How to Solve it by Computer‖ (Chaps 1-2), Prentice-Hall of India, 2002. 2. M. A. Weiss, ―Data Structures and Algorithm Analysis in C‖, 2nd ed, Pearson Education Asia, 2002. 3. Y. Langsam, M. J. Augenstein and A. M. Tenenbaum, ―Data Structures using C‖, Pearson Education Asia, 2004 4. Richard F. Gilberg, Behrouz A. Forouzan, ―Data Structures – A Pseudocode Approach with C‖, Thomson Brooks / COLE, 1998. 5. Aho, J. E. Hopcroft and J. D. Ullman, ―Data Structures and Algorithms‖, Pearson education Asia, 1983. 2 BLOCK I BLOCK I PROBLEM SOLVING Computer problem-solving can be summed up in one word – it is demanding! It is an intricate process requiring much thought, careful planning, logical precision, persistence, and attention to detail.