Showing papers on "Trie published in 1991"

An alternating digital tree (ADT) algorithm for 3D geometric searching and intersection problems

Abstract: A searching algorithm is presented for determining which members of a set of n points in an N dimensional space lie inside a prescribed space subregion. The algorithm is then extended to handle finite size objects as well as points. In this form it is capable of solving problems such as that of finding the objects from a given set which intersect with a prescribed object. The suitability of the algorithm is demonstrated for the problem of three dimensional unstructured mesh generation using the advancing front method.

On the height of digital trees and related problems

Abstract: This paper studies in a probabilistic framework some topics concerning the way words (strings) can overlap, and relationship of this to the height of digital trees associated with this set of words. A word is defined as a random sequence of (possibly infinite) symbols over a finite alphabet. A key notion of analignment matrix {Cij}i,j=1n is introduced whereCij is the length of the longest string that is a prefix of theith and thejth word. It is proved that the height of an associated digital tree is simply related to the alignment matrix through some order statistics. In particular, using this observation and proving some inequalities for order statistics, we establish that the height of adigital trie under anindependent model (i.e., all words are statistically independent) is asymptotically equal to 2 logźn wheren is the number of words stored in the trie and ź is a parameter of the probabilistic model. This result is generalized in three directions, namely we considerb-tries,Markovian model (i.e., dependency among letters in a word), and adependent model (i.e., dependency among words). In particular, when consecutive letters in a word are Markov dependent (Markovian model), then we demonstrate that the height converges in probability to 2 logźn where ź is a parameter of the underlying Markov chain. On the other hand, for suffix trees which fall into the dependent model, we show that the height does not exceed 2 logźn, where ź is a parameter of the probabilistic model. These results find plenty of applications in the analysis of data structures built over digital words.

Tree structure representation of an SQL clause

Abstract: A system and method for graphically representing a WHERE or HAVING clause of an SQL query directed to a relational database. Logical operators are defined and linked to predicates using a tree structure format (23). The tree is not binary in character and consequently exhibits a 1:1 relation between the predicates and tree leaves. The tree structure representation provides intuitive feedback to the user defining the query. Preferably the SQL format (24) and tree structure graphic format (23) queries appear simultaneously on the video display of the computer system used to define the query.

Implementing dynamic minimal-prefix tries

Abstract: A modified trie-searching algorithm and corresponding data structure are introduced which permit rapid search of a dictionary for a symbol or a valid abbreviation The dictionary-insertion algorithm automatically determines disambiguation points, where possible, for each symbol The search operation will classify a symbol as one of the following: unknown (ie not a valid symbol), ambiguous (ie is a prefix of more than one valid symbol) or known The search operation is performed in linear time proportional to the length of the input symbol, rather than the complexity of the trie An example implementation is given in the C programming language

Trie hashing with controlled load

Abstract: Trie hashing (TH), a primary key access method for storing and accessing records of dynamic files, is discussed. The key address is computed through a trie. A key search usually requires only one disk access when the trie is in core and two disk accesses for very large files when the trie must be on disk. A refinement to trie hashing, trie hashing with controlled load (THCL), is presented. It is designed to control the load factor of a TH file as tightly as that of a B-tree file, allows high load factor of up to 100% for ordered insertions, and increases the load factor for random insertions from 70% to over 85%. It is shown that these properties make trie hashing preferable to a B-tree. >

Tree Automata for Code Selection.

Abstract: We deal with the generation of code selectors in compiler backends. The fundamental concepts are systematically derived from the theory of regular tree grammars and finite tree automata. We use this general approach to construct algorithms that generalize and improve existing methods.

What can we learn about suffix trees from independent tries

Abstract: A suffix tree of a word is a digital tree that is built from suffixes of the underlying word. We consider words that are random sequences built from independent symbols over a finite alphabet. Our main finding shows that the depths in a suffix tree are asymptotically equivalent to the depths in a digital tree that stores independent keys (i.e., independent digital trees known also as tries). More precisely, we prove that the depths in a suffix tree build from the first n suffixes of a random word are normally distributed with the mean asymptotically equivalent to 1/h1 log n and the variance α·log n, where h1 is the entropy of the alphabet, and α is a parameter of the probabilistic model. Our results provide new insights into asymptotic properties of compression schemes, and therefore find direct applications in computer sciences and telecommunications, most notably in coding theory, theory of languages, and design and analysis of algorithms.

Keyword dictionary compression using efficient trie implementation

Abstract: Summary form only given. The author proposes a method to construct a compact and efficient tree structure which can be applied to both large- and small- scale keyword dictionaries. He uses four types of tree node representations eclectically depending on the number of children of the node, to minimize unused spaces and to provide fast access: array representation, bitmap director representation, list representation, and string representation. >

Method for pattern recognition

Abstract: An improved pattern recognition system, using an improved method for merging low-level recognition information with auxiliary contextual information such as a Deterministic Finite Automaton (DFA). The system comprises a low-level shape recognizer for handwriting input, an English Language dictionary organized as a Trie (a special type of DFA), and software to merge the results of the two. An input of digitized handwriting strokes is translated into characters using the shape recognizer and the Trie in tandem, allowing the system to reject nonsense translations at the earliest possible stage of the process and without the overhead traversing the trie from the top with each translation.