Wormhole: a Fast Ordered Index for In-Memory Data Management
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Application of TRIE Data Structure and Corresponding Associative Algorithms for Process Optimization in GRID Environment
Application of TRIE data structure and corresponding associative algorithms for process optimization in GRID environment V. V. Kashanskya, I. L. Kaftannikovb South Ural State University (National Research University), 76, Lenin prospekt, Chelyabinsk, 454080, Russia E-mail: a [email protected], b [email protected] Growing interest around different BOINC powered projects made volunteer GRID model widely used last years, arranging lots of computational resources in different environments. There are many revealed problems of Big Data and horizontally scalable multiuser systems. This paper provides an analysis of TRIE data structure and possibilities of its application in contemporary volunteer GRID networks, including routing (L3 OSI) and spe- cialized key-value storage engine (L7 OSI). The main goal is to show how TRIE mechanisms can influence de- livery process of the corresponding GRID environment resources and services at different layers of networking abstraction. The relevance of the optimization topic is ensured by the fact that with increasing data flow intensi- ty, the latency of the various linear algorithm based subsystems as well increases. This leads to the general ef- fects, such as unacceptably high transmission time and processing instability. Logically paper can be divided into three parts with summary. The first part provides definition of TRIE and asymptotic estimates of corresponding algorithms (searching, deletion, insertion). The second part is devoted to the problem of routing time reduction by applying TRIE data structure. In particular, we analyze Cisco IOS switching services based on Bitwise TRIE and 256 way TRIE data structures. The third part contains general BOINC architecture review and recommenda- tions for highly-loaded projects. -
KP-Trie Algorithm for Update and Search Operations
The International Arab Journal of Information Technology, Vol. 13, No. 6, November 2016 KP-Trie Algorithm for Update and Search Operations Feras Hanandeh1, Mohammed Akour2, Essam Al Daoud3, Rafat Alshorman4, Izzat Alsmadi5 1Dept. of Computer Information Systems, Faculty of Prince Al-Hussein Bin Abdallah II For Information Technology, Hashemite University, Zarqa, Jordan, [email protected] 2,5Dept. of Computer Information Systems, Faculty of Information Technology, Yarmouk University, Irbid, Jordan, [email protected], [email protected] 3,4Computer Science Department, Zarqa University [email protected]; [email protected] Abstract: Radix-Tree is a space optimized data structure that performs data compression by means of cluster nodes that share the same branch. Each node with only one child is merged with its child and is considered as space optimized. Nevertheless, it can't be considered as speed optimized because the root is associated with the empty string . Moreover, values are not normally associated with every node; they are associated only with leaves and some inner nodes that correspond to keys of interest. Therefore, it takes time in moving bit by bit to reach the desired word. In this paper we propose the KP-Trie which is consider as speed and space optimized data structure that is resulted from both horizontal and vertical compression. Keywords: Trie, radix tree, data structure, branch factor, indexing, tree structure, information retrieval. 1- Introduction The concept of Data structures such as trees has developed since the 19th century. Tries evolved from trees. They have different names Data structures are a specialized format for such as: Radix tree, prefix tree compact trie, efficient organizing, retrieving, saving and bucket trie, crit bit tree, and PATRICIA storing data. -
KP-Trie Algorithm for Update and Search Operations
The International Arab Journal of Information Technology, Vol. 13, No. 6, November 2016 722 KP-Trie Algorithm for Update and Search Operations Feras Hanandeh1, Izzat Alsmadi2, Mohammed Akour3, and Essam Al Daoud4 1Department of Computer Information Systems, Hashemite University, Jordan 2, 3Department of Computer Information Systems, Yarmouk University, Jordan 4Computer Science Department, Zarqa University, Jordan Abstract: Radix-Tree is a space optimized data structure that performs data compression by means of cluster nodes that share the same branch. Each node with only one child is merged with its child and is considered as space optimized. Nevertheless, it can’t be considered as speed optimized because the root is associated with the empty string. Moreover, values are not normally associated with every node; they are associated only with leaves and some inner nodes that correspond to keys of interest. Therefore, it takes time in moving bit by bit to reach the desired word. In this paper we propose the KP-Trie which is consider as speed and space optimized data structure that is resulted from both horizontal and vertical compression. Keywords: Trie, radix tree, data structure, branch factor, indexing, tree structure, information retrieval. Received January 14, 2015; accepted March 23, 2015; Published online December 23, 2015 1. Introduction the exception of leaf nodes, nodes in the trie work merely as pointers to words. Data structures are a specialized format for efficient A trie, also called digital tree, is an ordered multi- organizing, retrieving, saving and storing data. It’s way tree data structure that is useful to store an efficient with large amount of data such as: Large data associative array where the keys are usually strings, bases. -
Lecture 26 Fall 2019 Instructors: B&S Administrative Details
CSCI 136 Data Structures & Advanced Programming Lecture 26 Fall 2019 Instructors: B&S Administrative Details • Lab 9: Super Lexicon is online • Partners are permitted this week! • Please fill out the form by tonight at midnight • Lab 6 back 2 2 Today • Lab 9 • Efficient Binary search trees (Ch 14) • AVL Trees • Height is O(log n), so all operations are O(log n) • Red-Black Trees • Different height-balancing idea: height is O(log n) • All operations are O(log n) 3 2 Implementing the Lexicon as a trie There are several different data structures you could use to implement a lexicon— a sorted array, a linked list, a binary search tree, a hashtable, and many others. Each of these offers tradeoffs between the speed of word and prefix lookup, amount of memory required to store the data structure, the ease of writing and debugging the code, performance of add/remove, and so on. The implementation we will use is a special kind of tree called a trie (pronounced "try"), designed for just this purpose. A trie is a letter-tree that efficiently stores strings. A node in a trie represents a letter. A path through the trie traces out a sequence ofLab letters that9 represent : Lexicon a prefix or word in the lexicon. Instead of just two children as in a binary tree, each trie node has potentially 26 child pointers (one for each letter of the alphabet). Whereas searching a binary search tree eliminates half the words with a left or right turn, a search in a trie follows the child pointer for the next letter, which narrows the search• Goal: to just words Build starting a datawith that structure letter. -
Efficient In-Memory Indexing with Generalized Prefix Trees
Efficient In-Memory Indexing with Generalized Prefix Trees Matthias Boehm, Benjamin Schlegel, Peter Benjamin Volk, Ulrike Fischer, Dirk Habich, Wolfgang Lehner TU Dresden; Database Technology Group; Dresden, Germany Abstract: Efficient data structures for in-memory indexing gain in importance due to (1) the exponentially increasing amount of data, (2) the growing main-memory capac- ity, and (3) the gap between main-memory and CPU speed. In consequence, there are high performance demands for in-memory data structures. Such index structures are used—with minor changes—as primary or secondary indices in almost every DBMS. Typically, tree-based or hash-based structures are used, while structures based on prefix-trees (tries) are neglected in this context. For tree-based and hash-based struc- tures, the major disadvantages are inherently caused by the need for reorganization and key comparisons. In contrast, the major disadvantage of trie-based structures in terms of high memory consumption (created and accessed nodes) could be improved. In this paper, we argue for reconsidering prefix trees as in-memory index structures and we present the generalized trie, which is a prefix tree with variable prefix length for indexing arbitrary data types of fixed or variable length. The variable prefix length enables the adjustment of the trie height and its memory consumption. Further, we introduce concepts for reducing the number of created and accessed trie levels. This trie is order-preserving and has deterministic trie paths for keys, and hence, it does not require any dynamic reorganization or key comparisons. Finally, the generalized trie yields improvements compared to existing in-memory index structures, especially for skewed data. -
4 Hash Tables and Associative Arrays
4 FREE Hash Tables and Associative Arrays If you want to get a book from the central library of the University of Karlsruhe, you have to order the book in advance. The library personnel fetch the book from the stacks and deliver it to a room with 100 shelves. You find your book on a shelf numbered with the last two digits of your library card. Why the last digits and not the leading digits? Probably because this distributes the books more evenly among the shelves. The library cards are numbered consecutively as students sign up, and the University of Karlsruhe was founded in 1825. Therefore, the students enrolled at the same time are likely to have the same leading digits in their card number, and only a few shelves would be in use if the leadingCOPY digits were used. The subject of this chapter is the robust and efficient implementation of the above “delivery shelf data structure”. In computer science, this data structure is known as a hash1 table. Hash tables are one implementation of associative arrays, or dictio- naries. The other implementation is the tree data structures which we shall study in Chap. 7. An associative array is an array with a potentially infinite or at least very large index set, out of which only a small number of indices are actually in use. For example, the potential indices may be all strings, and the indices in use may be all identifiers used in a particular C++ program.Or the potential indices may be all ways of placing chess pieces on a chess board, and the indices in use may be the place- ments required in the analysis of a particular game. -
Search Trees for Strings a Balanced Binary Search Tree Is a Powerful Data Structure That Stores a Set of Objects and Supports Many Operations Including
Search Trees for Strings A balanced binary search tree is a powerful data structure that stores a set of objects and supports many operations including: Insert and Delete. Lookup: Find if a given object is in the set, and if it is, possibly return some data associated with the object. Range query: Find all objects in a given range. The time complexity of the operations for a set of size n is O(log n) (plus the size of the result) assuming constant time comparisons. There are also alternative data structures, particularly if we do not need to support all operations: • A hash table supports operations in constant time but does not support range queries. • An ordered array is simpler, faster and more space efficient in practice, but does not support insertions and deletions. A data structure is called dynamic if it supports insertions and deletions and static if not. 107 When the objects are strings, operations slow down: • Comparison are slower. For example, the average case time complexity is O(log n logσ n) for operations in a binary search tree storing a random set of strings. • Computing a hash function is slower too. For a string set R, there are also new types of queries: Lcp query: What is the length of the longest prefix of the query string S that is also a prefix of some string in R. Prefix query: Find all strings in R that have S as a prefix. The prefix query is a special type of range query. 108 Trie A trie is a rooted tree with the following properties: • Edges are labelled with symbols from an alphabet Σ. -
X-Fast and Y-Fast Tries
x-Fast and y-Fast Tries Outline for Today ● Bitwise Tries ● A simple ordered dictionary for integers. ● x-Fast Tries ● Tries + Hashing ● y-Fast Tries ● Tries + Hashing + Subdivision + Balanced Trees + Amortization Recap from Last Time Ordered Dictionaries ● An ordered dictionary is a data structure that maintains a set S of elements drawn from an ordered universe � and supports these operations: ● insert(x), which adds x to S. ● is-empty(), which returns whether S = Ø. ● lookup(x), which returns whether x ∈ S. ● delete(x), which removes x from S. ● max() / min(), which returns the maximum or minimum element of S. ● successor(x), which returns the smallest element of S greater than x, and ● predecessor(x), which returns the largest element of S smaller than x. Integer Ordered Dictionaries ● Suppose that � = [U] = {0, 1, …, U – 1}. ● A van Emde Boas tree is an ordered dictionary for [U] where ● min, max, and is-empty run in time O(1). ● All other operations run in time O(log log U). ● Space usage is Θ(U) if implemented deterministically, and O(n) if implemented using hash tables. ● Question: Is there a simpler data structure meeting these bounds? The Machine Model ● We assume a transdichotomous machine model: ● Memory is composed of words of w bits each. ● Basic arithmetic and bitwise operations on words take time O(1) each. ● w = Ω(log n). A Start: Bitwise Tries Tries Revisited ● Recall: A trie is a simple data 0 1 structure for storing strings. 0 1 0 1 ● Integers can be thought of as strings of bits. 1 0 1 1 0 ● Idea: Store integers in a bitwise trie. -
Tries and String Matching
Tries and String Matching Where We've Been ● Fundamental Data Structures ● Red/black trees, B-trees, RMQ, etc. ● Isometries ● Red/black trees ≡ 2-3-4 trees, binomial heaps ≡ binary numbers, etc. ● Amortized Analysis ● Aggregate, banker's, and potential methods. Where We're Going ● String Data Structures ● Data structures for storing and manipulating text. ● Randomized Data Structures ● Using randomness as a building block. ● Integer Data Structures ● Breaking the Ω(n log n) sorting barrier. ● Dynamic Connectivity ● Maintaining connectivity in an changing world. String Data Structures Text Processing ● String processing shows up everywhere: ● Computational biology: Manipulating DNA sequences. ● NLP: Storing and organizing huge text databases. ● Computer security: Building antivirus databases. ● Many problems have polynomial-time solutions. ● Goal: Design theoretically and practically efficient algorithms that outperform brute-force approaches. Outline for Today ● Tries ● A fundamental building block in string processing algorithms. ● Aho-Corasick String Matching ● A fast and elegant algorithm for searching large texts for known substrings. Tries Ordered Dictionaries ● Suppose we want to store a set of elements supporting the following operations: ● Insertion of new elements. ● Deletion of old elements. ● Membership queries. ● Successor queries. ● Predecessor queries. ● Min/max queries. ● Can use a standard red/black tree or splay tree to get (worst-case or expected) O(log n) implementations of each. A Catch ● Suppose we want to store a set of strings. ● Comparing two strings of lengths r and s takes time O(min{r, s}). ● Operations on a balanced BST or splay tree now take time O(M log n), where M is the length of the longest string in the tree. -
Prefix Hash Tree an Indexing Data Structure Over Distributed Hash
Prefix Hash Tree An Indexing Data Structure over Distributed Hash Tables Sriram Ramabhadran ∗ Sylvia Ratnasamy University of California, San Diego Intel Research, Berkeley Joseph M. Hellerstein Scott Shenker University of California, Berkeley International Comp. Science Institute, Berkeley and and Intel Research, Berkeley University of California, Berkeley ABSTRACT this lookup interface has allowed a wide variety of Distributed Hash Tables are scalable, robust, and system to be built on top DHTs, including file sys- self-organizing peer-to-peer systems that support tems [9, 27], indirection services [30], event notifi- exact match lookups. This paper describes the de- cation [6], content distribution networks [10] and sign and implementation of a Prefix Hash Tree - many others. a distributed data structure that enables more so- phisticated queries over a DHT. The Prefix Hash DHTs were designed in the Internet style: scala- Tree uses the lookup interface of a DHT to con- bility and ease of deployment triumph over strict struct a trie-based structure that is both efficient semantics. In particular, DHTs are self-organizing, (updates are doubly logarithmic in the size of the requiring no centralized authority or manual con- domain being indexed), and resilient (the failure figuration. They are robust against node failures of any given node in the Prefix Hash Tree does and easily accommodate new nodes. Most impor- not affect the availability of data stored at other tantly, they are scalable in the sense that both la- nodes). tency (in terms of the number of hops per lookup) and the local state required typically grow loga- Categories and Subject Descriptors rithmically in the number of nodes; this is crucial since many of the envisioned scenarios for DHTs C.2.4 [Comp. -
Hash Tables & Searching Algorithms
Search Algorithms and Tables Chapter 11 Tables • A table, or dictionary, is an abstract data type whose data items are stored and retrieved according to a key value. • The items are called records. • Each record can have a number of data fields. • The data is ordered based on one of the fields, named the key field. • The record we are searching for has a key value that is called the target. • The table may be implemented using a variety of data structures: array, tree, heap, etc. Sequential Search public static int search(int[] a, int target) { int i = 0; boolean found = false; while ((i < a.length) && ! found) { if (a[i] == target) found = true; else i++; } if (found) return i; else return –1; } Sequential Search on Tables public static int search(someClass[] a, int target) { int i = 0; boolean found = false; while ((i < a.length) && !found){ if (a[i].getKey() == target) found = true; else i++; } if (found) return i; else return –1; } Sequential Search on N elements • Best Case Number of comparisons: 1 = O(1) • Average Case Number of comparisons: (1 + 2 + ... + N)/N = (N+1)/2 = O(N) • Worst Case Number of comparisons: N = O(N) Binary Search • Can be applied to any random-access data structure where the data elements are sorted. • Additional parameters: first – index of the first element to examine size – number of elements to search starting from the first element above Binary Search • Precondition: If size > 0, then the data structure must have size elements starting with the element denoted as the first element. In addition, these elements are sorted. -
Introduction to Hash Table and Hash Function
Introduction to Hash Table and Hash Function This is a short introduction to Hashing mechanism Introduction Is it possible to design a search of O(1)– that is, one that has a constant search time, no matter where the element is located in the list? Let’s look at an example. We have a list of employees of a fairly small company. Each of 100 employees has an ID number in the range 0 – 99. If we store the elements (employee records) in the array, then each employee’s ID number will be an index to the array element where this employee’s record will be stored. In this case once we know the ID number of the employee, we can directly access his record through the array index. There is a one-to-one correspondence between the element’s key and the array index. However, in practice, this perfect relationship is not easy to establish or maintain. For example: the same company might use employee’s five-digit ID number as the primary key. In this case, key values run from 00000 to 99999. If we want to use the same technique as above, we need to set up an array of size 100,000, of which only 100 elements will be used: Obviously it is very impractical to waste that much storage. But what if we keep the array size down to the size that we will actually be using (100 elements) and use just the last two digits of key to identify each employee? For example, the employee with the key number 54876 will be stored in the element of the array with index 76.