DOCSLIB.ORG

Suffix Trees for Fast Sensor Data Forwarding

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Suffix Trees for Fast Sensor Data Forwarding Jui-Chieh Wub Hsueh-I Lubc Polly Huangac Department of Electrical Engineeringa Department of Computer Science and Information Engineeringb Graduate Institute of Networking and Multimediac National Taiwan University [email protected], [email protected], [email protected] Abstract— In data-centric wireless sensor networks, data are alleviates the effort of node addressing and address reconfig- no longer sent by the sink node’s address. Instead, the sink uration in large-scale mobile sensor networks. node sends an explicit interest for a particular type of data. The source and the intermediate nodes then forward the data Forwarding in data-centric sensor networks is particularly according to the routing states set by the corresponding interest. challenging. It involves matching of the data content, i.e., This data-centric style of communication is promising in that it string-based attributes and values, instead of numeric ad- alleviates the effort of node addressing and address reconfigura- dresses. This content-based forwarding problem is well studied tion. However, when the number of interests from different sinks in the domain of publish-subscribe systems. It is estimated increases, the size of the interest table grows. It could take 10s to 100s milliseconds to match an incoming data to a particular in [3] that the time it takes to match an incoming data to a interest, which is orders of mangnitude higher than the typical particular interest ranges from 10s to 100s milliseconds. This transmission and propagation delay in a wireless sensor network. processing delay is several orders of magnitudes higher than The interest table lookup process is the bottleneck of packet the propagation and transmission delay. forwarding delay and the most time consuming part is the Consider the MicaZ [4] and TinyOS [5] sensor network repeated string matching involved. Motivated to enable fast sensor data forwarding, we study and evaluate the use of an development platform. The packet size limit is 36 bytes. The efficient data structure, suffix tree (ST), for fast string matching wireless radio transmits at 100s kbps. The transmission delay in resource-limited sensor networks. Results of our experiments is thus at the scale of 1s milliseconds. Assume 10 meter radio show that ST is faster than the state of the art by up to 29% range and 2 ∗ 108 m/s propagation speed The propagation for identifying a match and 48% for identifying a non-match. delay can be found at the scale of 0.01s microseconds. The Further with a novel space optimization scheme, the memory space requirement for ST is reduced by up to 24% which makes processing delay is evidently the bottleneck of the per hop ST feasible to run on resource-limited sensor nodes. forwarding delay. The interest lookup delay is contributed by 2 levels of I. INTRODUCTION matching - interest and predicate matching. Each interest may consist of multiple predicates. At the higher level, the On the address-centric Internet, communication nodes are system needs to identify, among various interests, a particular numerically addressed, for example, 140.112.42.220.A source interest that matches the incoming data. At the lower level, node sends data by the destination node’s address. Forwarding, the system verifies whether a predicate in an interest matches also known as the routing table lookup problem, involves how, given the destination address of an incoming data packet, each intermediate router locates a matching entry in the routing table. From the matching entry, the router identifies the network interfaces (or ports) towards the next hops that the data packet should be forwarded further. Efficient algorithms and data structures such as [1] are proposed to speed up the number matching, which lead to the design of very high-speed IP switches today. Motivated to achieve high-speed forwarding for sensor networks, we seek efficient algorithms and data structures to speed up string matching for data-centric sensor networks. In data-centric wireless sensor networks [2], nodes are no longer addressed. Data do not carry the destination address. Instead, each sink node sends an explicit interest through the network to draw in a particular type of data. The intermediate nodes in turn disseminate the data based on the data content rather than the destination node’s address. This data-centric style of communication is particularly promising for that it Fig. 1. An example of interest matching the incoming data. Illustrated in Fig 1 are 3 example interests we implement three string matching algorithms and evaluate composed by a number of predicates. Interest 1 is looking for how well they will perform in practice. The remainder of this anything related to the nslab group. Interest 2 looks for data paper is organized as follows. The related work is presented about a faculty member whose name is polly, and interest 3 next in Section II. We describe then in Section III the string looks for data about all 2nd year and above master students. matching algorithms. Next in Section IV, we provide an The incoming data in Fig 1 matches both interest 1 and 2. analytical comparison of the algorithms. In Section V, VI, and Much of the recent work [6][7][8][9] has focus on the VII we detail the experimental setup, results, and our findings strategies of structuring interests or content types to enable on how the algorithms perform in practice. fast interest matching. Their objective is to reduce the number of predicate matching required. Our work complements these II. RELATED WORK earlier studies in that we focus on improving the efficiency of A. Data-Centric Communication individual predicate matching. In the traditional IP network, nodes communicate to each Predicate matching involves attribute matching and value other by the fixed IP addresses. This communication model matching. Attribute matching is essentially an exact string is proven, by the daily operation of Internet, effective in matching problem. One common practice to speed up attribute supporting applications running on static and full-fledged com- matching is to fix the bit position of all possible attributes in puters. For mobile and resource-limited sensor networks, how the data packet as well as the routing table. This method, to configure and reconfigure node addresses in the precense of although simplifies the attribute matching process, will be node dynamics poses a great challenge. This problem is first memory and bandwidth consuming when the number of differ- raised and addressed in one of the pioneer work on sensor ent data types is high. When there are different sensors to be networks [2]. In that, the authors propose the data-centric added to the network, the system will not be easily extendable communication paradigm. without changing the packet format and interest table data In data-centric communication, digital information are dis- structure. Value matching is also a string matching problem, seminated based on the feature/attribute/content of the infor- when the data type is string. Depending on the operator of mation itself, not the addresses of issuers or receivers. In the predicate, value matching may require exact or sub-string the first data-centric routing mechanism for wireless sensor matching. In essence, the efficiency of predicate is determined networks [12], sinks send explicit interest packets to set up by the efficiency of the string matching algorithm used. routing states at the intermediate nodes. These interest specific For efficient string matching, prior work [13] suggests the routing states in turn draw in the data of interest for the sinks. use of ternary search tree (TST). It is a string matching Such dissemination scheme relies on well-defined naming algorithm with O(|P | + log(N)) time complexity and O(|S|) system to describe data attributes and sink interests. The space complexity. P denotes the input string, typically an corresponding naming system and the filter-based forwarding attribute or value string in the incoming data. S denotes the mechanism are detailed in [6]. The string maching problem, training word set which concatenates all the strings appear although recognized as the performance bottleneck, is not in the entire interest table. N denotes the total number of addressed. strings in the training set. To speed up the string matching process further, we propose and evaluate the use of suffix B. Publish/Subscribe Systems tree (ST), a linear time string matching algorithm that can In [13][14], the authors design a set of efficient forwarding be easily extended to perform efficient prefix, suffix and and routing mechanisms for content-based data dissemina- substring matching. ST has an O(|P |) time and O(|S|) space tion. The notion of content-based communication is essen- complexity [10][11]. tially the same as data-centric communication. The mech- Although the large-scale performance of TST and ST’s anisms proposed, although descends from the literature of memory requirement is the same, we find, in real implemen- publish/subscribe systems, are applicable to sensor networks. tations, the amount of memory required by ST is significantly There are two different kinds of publish/subscribe systems: higher than that of TST. This is a serious problem for sensor channel-based and content-based. In both systems, multiple nodes in which the memory space is very limited. To tackle users may subscribe to the data of interest. In channel- the problem, we further propose a scheme to optimize the based systems, the users subscribe to a particular channel and memory consumption for ST. the corresponding data broker pushes particular data to the To observe how the algorithms will perform in practice, channel from which the subscribing users receive the data. In we implement TST and ST, as well as a simple hash-based content-based systems, the concept of channel is refined as method for comparison.
Recommended publications
  • Compressed Suffix Trees with Full Functionality

    Compressed Suffix Trees with Full Functionality

    Compressed Suffix Trees with Full Functionality Kunihiko Sadakane Department of Computer Science and Communication Engineering, Kyushu University Hakozaki 6-10-1, Higashi-ku, Fukuoka 812-8581, Japan [email protected] Abstract We introduce new data structures for compressed suffix trees whose size are linear in the text size. The size is measured in bits; thus they occupy only O(n log |A|) bits for a text of length n on an alphabet A. This is a remarkable improvement on current suffix trees which require O(n log n) bits. Though some components of suffix trees have been compressed, there is no linear-size data structure for suffix trees with full functionality such as computing suffix links, string-depths and lowest common ancestors. The data structure proposed in this paper is the first one that has linear size and supports all operations efficiently. Any algorithm running on a suffix tree can also be executed on our compressed suffix trees with a slight slowdown of a factor of polylog(n). 1 Introduction Suffix trees are basic data structures for string algorithms [13]. A pattern can be found in time proportional to the pattern length from a text by constructing the suffix tree of the text in advance. The suffix tree can also be used for more complicated problems, for example finding the longest repeated substring in linear time. Many efficient string algorithms are based on the use of suffix trees because this does not increase the asymptotic time complexity. A suffix tree of a string can be constructed in linear time in the string length [28, 21, 27, 5].
  • Suffix Trees

    Suffix Trees

    JASS 2008 Trees - the ubiquitous structure in computer science and mathematics Suffix Trees Caroline L¨obhard St. Petersburg, 9.3. - 19.3. 2008 1 Contents 1 Introduction to Suffix Trees 3 1.1 Basics . 3 1.2 Getting a first feeling for the nice structure of suffix trees . 4 1.3 A historical overview of algorithms . 5 2 Ukkonen’s on-line space-economic linear-time algorithm 6 2.1 High-level description . 6 2.2 Using suffix links . 7 2.3 Edge-label compression and the skip/count trick . 8 2.4 Two more observations . 9 3 Generalised Suffix Trees 9 4 Applications of Suffix Trees 10 References 12 2 1 Introduction to Suffix Trees A suffix tree is a tree-like data-structure for strings, which affords fast algorithms to find all occurrences of substrings. A given String S is preprocessed in O(|S|) time. Afterwards, for any other string P , one can decide in O(|P |) time, whether P can be found in S and denounce all its exact positions in S. This linear worst case time bound depending only on the length of the (shorter) string |P | is special and important for suffix trees since an amount of applications of string processing has to deal with large strings S. 1.1 Basics In this paper, we will denote the fixed alphabet with Σ, single characters with lower-case letters x, y, ..., strings over Σ with upper-case or Greek letters P, S, ..., α, σ, τ, ..., Trees with script letters T , ... and inner nodes of trees (that is, all nodes despite of root and leaves) with lower-case letters u, v, ...
  • Search Trees

    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..
  • Lecture 1: Introduction

    Lecture 1: Introduction

    Lecture 1: Introduction Agenda: • Welcome to CS 238 — Algorithmic Techniques in Computational Biology • Official course information • Course description • Announcements • Basic concepts in molecular biology 1 Lecture 1: Introduction Official course information • Grading weights: – 50% assignments (3-4) – 50% participation, presentation, and course report. • Text and reference books: – T. Jiang, Y. Xu and M. Zhang (co-eds), Current Topics in Computational Biology, MIT Press, 2002. (co-published by Tsinghua University Press in China) – D. Gusfield, Algorithms for Strings, Trees, and Sequences: Computer Science and Computational Biology, Cambridge Press, 1997. – D. Krane and M. Raymer, Fundamental Concepts of Bioin- formatics, Benjamin Cummings, 2003. – P. Pevzner, Computational Molecular Biology: An Algo- rithmic Approach, 2000, the MIT Press. – M. Waterman, Introduction to Computational Biology: Maps, Sequences and Genomes, Chapman and Hall, 1995. – These notes (typeset by Guohui Lin and Tao Jiang). • Instructor: Tao Jiang – Surge Building 330, x82991, [email protected] – Office hours: Tuesday & Thursday 3-4pm 2 Lecture 1: Introduction Course overview • Topics covered: – Biological background introduction – My research topics – Sequence homology search and comparison – Sequence structural comparison – string matching algorithms and suffix tree – Genome rearrangement – Protein structure and function prediction – Phylogenetic reconstruction * DNA sequencing, sequence assembly * Physical/restriction mapping * Prediction of regulatiory elements • Announcements:
  • Design and Analysis of Data Structures

    Design and Analysis of Data Structures

    Contents 1 Introduction and Review 1 1.1 Welcome! . .1 1.2 Tick Tock, Tick Tock . .2 1.3 Classes of Computational Complexity . .6 1.4 The Fuss of C++ . 12 1.5 Random Numbers . 30 1.6 Bit-by-Bit . 33 1.7 The Terminal-ator . 38 1.8 Git, the \Undo" Button of Software Development . 43 2 Introductory Data Structures 47 2.1 Array Lists . 47 2.2 Linked Lists . 53 2.3 Skip Lists . 59 2.4 Circular Arrays . 67 2.5 Abstract Data Types . 75 2.6 Deques . 76 2.7 Queues . 79 2.8 Stacks . 81 2.9 And the Iterators Gonna Iterate-ate-ate . 84 3 Tree Structures 91 3.1 Lost in a Forest of Trees . 91 3.2 Heaps . 99 3.3 Binary Search Trees . 105 3.4 BST Average-Case Time Complexity . 112 3.5 Randomized Search Trees . 117 3.6 AVL Trees . 125 3.7 Red-Black Trees . 136 3.8 B-Trees . 145 3.9 B+ Trees . 156 i ii CONTENTS 4 Introduction to Graphs 167 4.1 Introduction to Graphs . 167 4.2 Graph Representations . 173 4.3 Algorithms on Graphs: Breadth First Search . 177 4.4 Algorithms on Graphs: Depth First Search . 181 4.5 Dijkstra's Algorithm . 185 4.6 Minimum Spanning Trees . 190 4.7 Disjoint Sets . 197 5 Hashing 209 5.1 The Unquenched Need for Speed . 209 5.2 Hash Functions . 210 5.3 Introduction to Hash Tables . 215 5.4 Probability of Collisions . 221 5.5 Collision Resolution: Open Addressing . 227 5.6 Collision Resolution: Closed Addressing .
  • Suffix Trees and Suffix Arrays in Primary and Secondary Storage Pang Ko Iowa State University

    Suffix Trees and Suffix Arrays in Primary and Secondary Storage Pang Ko Iowa State University

    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 2007 Suffix trees and suffix arrays in primary and secondary storage Pang Ko Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Bioinformatics Commons, and the Computer Sciences Commons Recommended Citation Ko, Pang, "Suffix trees and suffix arrays in primary and secondary storage" (2007). Retrospective Theses and Dissertations. 15942. https://lib.dr.iastate.edu/rtd/15942 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Suffix trees and suffix arrays in primary and secondary storage by Pang Ko A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Computer Engineering Program of Study Committee: Srinivas Aluru, Major Professor David Fern´andez-Baca Suraj Kothari Patrick Schnable Srikanta Tirthapura Iowa State University Ames, Iowa 2007 UMI Number: 3274885 UMI Microform 3274885 Copyright 2007 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI 48106-1346 ii DEDICATION To my parents iii TABLE OF CONTENTS LISTOFTABLES ................................... v LISTOFFIGURES .................................. vi ACKNOWLEDGEMENTS. .. .. .. .. .. .. .. .. .. ... .. .. .. .. vii ABSTRACT....................................... viii CHAPTER1. INTRODUCTION . 1 1.1 SuffixArrayinMainMemory .
  • Final Review

    Final Review

    Final Review 1 Final Exam (Out of 70) • Part A: Basic knowledge of data structures – 20 points – MulEple choice • Part B: Applicaon, Comparison and Implementaon of the data structures – 20 points – Apply supported operaons (like find and insert) to data structures we have covered like: BST, AVL, RBTs, MulEway trie, Ternary Trie, B trees, skip lists. Also essenEal concepts in Huffman codes • Part C: Simulang algorithms and run Eme analysis – 15 points – Graph algorithms: BFS, DFS, Dijkstra, Prims’, Kruskals’. Also union find • Part D: C++ and programming assignments – 15 points – Short answer 2 Final Exam Practice Questions CSE 100 (Fall 2014) CSE Department University of California, San Diego Part A: The Basics This section tests your basic knowledge of data structures via multiple choice questions. Sample questions include all the iclicker and reading quiz questions covered in class. Please make sure you review them. Part B: Application, Comparison and Implementation This section tests how well you understand what goes on under the hood of the data structures covered during the course, their strengths and weaknesses and their applications. The format is short answers and fill in the blanks. 1. B-trees. (a) Construct a 2-3 tree by inserting the following keys in the order shown: 10, 15, 20, 25, 17, 30. You can check your answers and experiment with trees of your own design at the following web sites: https://www.cs.usfca.edu/˜galles/visualization/BTree.html B-trees http://ats.oka.nu/b-tree/b-tree.manual.html (b) Which of the following are legal 2,3 trees (B tree of order 3)? For a tree that is not a valid 2,3 tree, state a reason why.
  • Finger Search Trees

    Finger Search Trees

    11 Finger Search Trees 11.1 Finger Searching....................................... 11-1 11.2 Dynamic Finger Search Trees ....................... 11-2 11.3 Level Linked (2,4)-Trees .............................. 11-3 11.4 Randomized Finger Search Trees ................... 11-4 Treaps • Skip Lists 11.5 Applications............................................ 11-6 Optimal Merging and Set Operations • Arbitrary Gerth Stølting Brodal Merging Order • List Splitting • Adaptive Merging and University of Aarhus Sorting 11.1 Finger Searching One of the most studied problems in computer science is the problem of maintaining a sorted sequence of elements to facilitate efficient searches. The prominent solution to the problem is to organize the sorted sequence as a balanced search tree, enabling insertions, deletions and searches in logarithmic time. Many different search trees have been developed and studied intensively in the literature. A discussion of balanced binary search trees can e.g. be found in [4]. This chapter is devoted to finger search trees which are search trees supporting fingers, i.e. pointers, to elements in the search trees and supporting efficient updates and searches in the vicinity of the fingers. If the sorted sequence is a static set of n elements then a simple and space efficient representation is a sorted array. Searches can be performed by binary search using 1+⌊log n⌋ comparisons (we throughout this chapter let log x denote log2 max{2, x}). A finger search starting at a particular element of the array can be performed by an exponential search by inspecting elements at distance 2i − 1 from the finger for increasing i followed by a binary search in a range of 2⌊log d⌋ − 1 elements, where d is the rank difference in the sequence between the finger and the search element.
  • Lecture Notes of CSCI5610 Advanced Data Structures

    Lecture Notes of CSCI5610 Advanced Data Structures

    Lecture Notes of CSCI5610 Advanced Data Structures Yufei Tao Department of Computer Science and Engineering Chinese University of Hong Kong July 17, 2020 Contents 1 Course Overview and Computation Models 4 2 The Binary Search Tree and the 2-3 Tree 7 2.1 The binary search tree . .7 2.2 The 2-3 tree . .9 2.3 Remarks . 13 3 Structures for Intervals 15 3.1 The interval tree . 15 3.2 The segment tree . 17 3.3 Remarks . 18 4 Structures for Points 20 4.1 The kd-tree . 20 4.2 A bootstrapping lemma . 22 4.3 The priority search tree . 24 4.4 The range tree . 27 4.5 Another range tree with better query time . 29 4.6 Pointer-machine structures . 30 4.7 Remarks . 31 5 Logarithmic Method and Global Rebuilding 33 5.1 Amortized update cost . 33 5.2 Decomposable problems . 34 5.3 The logarithmic method . 34 5.4 Fully dynamic kd-trees with global rebuilding . 37 5.5 Remarks . 39 6 Weight Balancing 41 6.1 BB[α]-trees . 41 6.2 Insertion . 42 6.3 Deletion . 42 6.4 Amortized analysis . 42 6.5 Dynamization with weight balancing . 43 6.6 Remarks . 44 1 CONTENTS 2 7 Partial Persistence 47 7.1 The potential method . 47 7.2 Partially persistent BST . 48 7.3 General pointer-machine structures . 52 7.4 Remarks . 52 8 Dynamic Perfect Hashing 54 8.1 Two random graph results . 54 8.2 Cuckoo hashing . 55 8.3 Analysis . 58 8.4 Remarks . 59 9 Binomial and Fibonacci Heaps 61 9.1 The binomial heap .
  • String Algorithm

    String Algorithm

    Trie: A data-structure for a set of words All words over the alphabet Σ={a,b,..z}. In the slides, let say that the alphabet is only {a,b,c,d} S – set of words = {a,aba, a, aca, addd} Need to support the operations Tries and suffixes trees • insert(w) – add a new word w into S. • delete(w) – delete the word w from S. • find(w) is w in S ? Alon Efrat • Future operation: Computer Science Department • Given text (many words) where is w in the text. University of Arizona • The time for each operation should be O(k), where k is the number of letters in w • Usually each word is associated with addition info – not discussed here. 2 Trie (Tree+Retrive) for S A trie - example p->ar[‘b’-’a’] Note: The label of an edge is the label of n A tree where each node is a struct consist the cell from which this edge exits n Struct node { p a b c d n char[4] *ar; 0 a n char flag ; /* 1 if a word ends at this node. b d Otherwise 0 */ a b c d a b c d Corresponding to w=“d” } a b c d a b c d flag 1 1 0 ar 1 b Corr. To w=“db” (not in S, flag=0) S={a,b,dbb} a b c d 0 a b c d flag ar 1 b Rule: a b c d Corr. to w= dbb Each node corresponds to a word w 1 “ ” (w which is in S iff the flag is 1) 3 In S, so flag=1 4 1 Finding if word w is in the tree Inserting a word w p=root; i =0 Recall – we need to modify the tree so find(w) would return While(1){ TRUE.
  • Pointer-Machine Algorithms for Fully-Online Construction of Suffix

    Pointer-Machine Algorithms for Fully-Online Construction of Suffix

    Pointer-Machine Algorithms for Fully-Online Construction of Suffix Trees and DAWGs on Multiple Strings Shunsuke Inenaga Department of Informatics, Kyushu University, Japan PRESTO, Japan Science and Technology Agency, Japan [email protected] Abstract. We deal with the problem of maintaining the suffix tree indexing structure for a fully-online collection of strings, where a new character can be prepended to any string in the collection at any time. The only previously known algorithm for the problem, recently proposed by Takagi et al. [Algorithmica 82(5): 1346-1377 (2020)], runs in O(N log σ) time and O(N) space on the word RAM model, where N denotes the total length of the strings and σ denotes the alphabet size. Their algorithm makes heavy use of the nearest marked ancestor (NMA) data structure on semi-dynamic trees, that can answer queries and supports insertion of nodes in O(1) amortized time on the word RAM model. In this paper, we present a simpler fully-online right-to-left algorithm that builds the suffix tree for a given string collection in O(N(log σ + log d)) time and O(N) space, where d is the maximum number of in-coming Weiner links to a node of the suffix tree. We note that d is bounded by the height of the suffix tree, which is further bounded by the length of the longest string in the collection. The advantage of this new algorithm is that it works on the pointer machine model, namely, it does not use the complicated NMA data structures that involve table look-ups.
  • Analysis of Algorithms and Data Structures for Text Indexing

    Analysis of Algorithms and Data Structures for Text Indexing

    ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ FAKULTÄT FÜR INFORMATIK ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ TECHNISCHE UNIVERSITÄT MÜNCHEN Lehrstuhl für Effiziente Algorithmen Analysis of Algorithms and Data Structures for Text Indexing Moritz G. Maaß ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ FAKULTÄT FÜR INFORMATIK ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ TECHNISCHE UNIVERSITÄT MÜNCHEN Lehrstuhl für Effiziente Algorithmen Analysis of Algorithms and Data Structures for Text Indexing Moritz G. Maaß Vollständiger Abdruck der von der Fakultät für Informatik der Technischen Universität München zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzender: Univ.-Prof. Dr. Dr. h.c. mult. Wilfried Brauer Prüfer der Dissertation: 1. Univ.-Prof. Dr. Ernst W. Mayr 2. Prof. Robert Sedgewick, Ph.D. (Princeton University, New Jersey, USA) Die Dissertation wurde am 12. April 2005 bei der Technischen Universität München eingereicht und durch die Fakultät für Informatik am 26. Juni 2006 angenommen. Abstract Large amounts of textual data like document collections, DNA sequence data, or the Internet call for fast look-up methods that avoid searching the whole corpus. This is often accomplished using tree-based data structures for text indexing such as tries, PATRICIA trees, or suffix trees. We present and analyze improved algorithms and index data structures for exact and error-tolerant search. Affix trees are a data structure for exact indexing. They are a generalization of suffix trees, allowing a bidirectional search by extending a pattern to the left and to the right during retrieval. We present an algorithm that constructs affix trees on-line in both directions, i.e., by augmenting the underlying string in both directions. An amortized analysis yields that the algorithm has a linear-time worst-case complexity. A space efficient method for error-tolerant searching in a dictionary for a pattern allowing some mismatches can be implemented with a trie or a PATRICIA tree.