. Initially introduced in the late 1960s and early 1970s, dynamic programming algorithms have become increasingly popular in automatic speech recognition. There are two reasons why this has occurred: First, the dynamic programming strategy can be combined with avery e#cient and practical pruning strategy so that very large search spaces can be handled. Second, the dynamic programming strategy has turned out to be extremely #exible in adapting to new requirements. Examples of such requirements are the lexical tree organization of the pronunciation lexicon and the generation of a word graph instead of the single best sentence. In this paper, we attempt to systematically review the use of dynamic programming search strategies for small#vocabulary and large#vocabulary continuous speech recognition. The following methods are described in detail: search using a linear lexicon, search using a lexical tree, language-model look-ahead and word graph generation. 1 Introduction Search strategie...

The authors are developing an automated reverse engineering system for reconstructing the shape of simple mechanical parts. B-rep models are created by fitting surfaces to point clouds obtained by scanning an object using a 3D laser scanner. The resulting models, although valid, are often not suitable for purposes such as redesign because expected regularities and constraints are not present. This information is lost because each face of the model is determined independently. A global approach is required, in particular one that is capable of finding symmetries originally present. This paper describes a practical algorithm for finding global symmetries in suitable B-rep models built from planes, spheres, cylinders, cones and tori. It has been implemented and used to determine approximate symmetries of models with up to about 200 vertices in reasonable time. The time performance of the algorithm in the worst case is bounded by O(n^3.5 log^4 n), and a justification is given that on common engineering objects it takes about O(n^2 log^4 n), making it a practical tool for use in a reverse engineering package. Details of the algorithm are given, along with some results from a number of illustrative test runs.

This paper explores the structure of red-black trees by solving an apparently simple problem: given an ascending sequence of elements, construct a red-black tree which contains the elements in symmetric order. Several extreme red-black tree shapes are characterized: trees of minimum and maximum height, trees with a minimal and with a maximal proportion of red nodes. These characterizations are obtained by relating tree shapes to various number systems. In addition, connections to left-complete trees, AVL trees, and half-balanced trees are highlighted. 1 Introduction Red-black trees are an elegant search-tree scheme that guarantees O(log n) worstcase running time of basic dynamic-set operations. Recently, C. Okasaki (1998; 1999) presented an impressively simple functional implementation of red-black trees. In this paper we plunge deeper into the structure of red-black trees by solving an apparently simple problem: given an ascending sequence of elements, construct a red-black tree whic...

Subset construction is the method of converting a nondeterministic finite-state machine into a deterministic one. The process of determinization is an important one in any implementation of finite-state machines since nondeterministic machines are often easier to describe than their deterministic equivalents and the conversion of regular expressions to finite-state machines usually produces nondeterministic machines. We discuss one aspect of subset construction; namely, the computation of the instructions of the equivalent deterministic machine. Although the discussion is to some extent independent of any specific assumptions, we draw some conclusions within the context of INR and Grail, both packages for the manipulation of finite-state machines. The aim of the discussion is to present the problem and suggest some possible solutions; we do not intend to and cannot be definitive since much remains unknown. z This research was supported by grants from the Natural Sciences and Engineeri...

1.1 Representations in problem solving....................... 4

this paper we present a discrete relaxation algorithm for reducing the intrinsic combinatorial complexity by pruning the decision tree based on unreliable prior information from independent 2D-tracking for each view. The algorithm improves the reliability of spatio-temporal correspondence by simultaneous optimisation over multiple views in the case where 2D-tracking in one or more views are ambiguous. Application to the 3D reconstruction of human movement, based on tracking of skin-coloured regions in three views, demonstrates considerable improvement in reliability and performance. Results demonstrate that the optimisation over multiple views gives correct 3D reconstruction and object labeling in the presence of incorrect 2D-tracking whilst maintaining real-time performance

A string x is an outfix of a string y if there is a string w such that x1wx2 = y, wherex = x1x2 and a set X of strings is outfix-free if no string in X is an outfix of any other string in X. We examine the outfix-free regular languages. Based on the properties of outfix strings, we develop a polynomial-time algorithm that determines the outfix-freeness of regular languages. We consider two cases: A language is given as a set of strings and a language is given by an acyclic deterministic finite-state automaton. Furthermore, we investigate the prime outfix-free decomposition of outfix-free regular languages and design a linear-time prime outfix-free decomposition algorithm for outfix-free regular languages. We demonstrate the uniqueness of prime outfix-free decomposition.

Trie hashing is a scheme, proposed by Litwin, for indexing records with very long alphanumeric keys. The records are grouped into buckets of capacity b and maintained on secondary storage. To retrieve a record, the memory resident trie is traversed from the root to a leaf node where the address of the target bucket is found. Using the address found, the data bucket is read into memory and searched to determine the presence or absence of the record. The scheme, for all practical purposes, locates a record in one or two disk accesses. Unlike a trie, the scheme proposed suffers from potential degeneracy when the keys inserted are ordered and has an expensive reconstruction cost if a system failure occurs during a session. We present a new approach to implementing Trie Hashing that resolves the degeneracy problem. Our approach combines the basic trie hashing algorithm with the balancing techniques of the Red-Black Binary Search Tree, to produce a relatively balanced trie hashing scheme. As...

This paper describes algorithms for key deletion in B+-trees. There are published algorithms and pseudocode for searching and inserting keys, but deletion, due to its greater complexity and perceived lesser importance, is glossed over completely or left as an exercise to the reader. To remedy this situation, we provide a well documented flowchart, algorithm, and pseudo-code for deletion, their relation to search and insertion algorithms, and a reference to a freely available, complete B+-tree library written in the C programming language.

Introduction The study of data structures, i.e., methods for organizing data that are suitable for computer processing, is one of the classic topics of computer science. At the hardware level, a computer views storage devices such as internal memory and disk as holders of elementary data units (bytes), each accessible through its address (an integer). When writing programs, instead of manipulating the data at the byte level, it is convenient to organize them into higher level entities, called data structures. Most data structures can be viewed as containers that store a collection of objects of a given type, called the elements of the container. Often a total order is defined among the elements (e.g., alphabetically ordered names, points in the plane ordered by x-coordinate). A data structure has an associated repertory of operations, classified into queries, which retrieve information on the dat