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Showing papers on "Tree (data structure) published in 1989"


Journal ArticleDOI
TL;DR: In this paper, a general-purpose code for evolving three-dimensional, self-gravitating fluids in astrophyics, both with and without collisionless matter, is described.
Abstract: A new, general-purpose code for evolving three-dimensional, self-gravitating fluids in astrophyics, both with and without collisionless matter, is described. In this TREESPH code, hydrodynamic properties are determined using a Monte Carlo-like approach known as smoothed particle hydrodynamics (SPH). Unlike most previous implementations of SPH, gravitational forces are computed with a hierarchical tree algorithm. Multiple expansions are used to approximate the potential of distant groups of particles, reducing the cost per step. More significantly, the improvement in efficiency is achieved without the introduction of a grid. A unification of SPH with the hierarchical tree method is a natural way of allowing for larger N within a Lagrangian framework. The data structures used to manipulate the grouping of particles can be applied directly to certain aspects of the SPH calculation. 75 refs.

1,034 citations


Journal ArticleDOI
TL;DR: This paper compares five methods for pruning decision trees, developed from sets of examples, and shows that three methods—critical value, error complexity and reduced error—perform well, while the other two may cause problems.
Abstract: This paper compares five methods for pruning decision trees, developed from sets of examples. When used with uncertain rather than deterministic data, decision-tree induction involves three main stages—creating a complete tree able to classify all the training examples, pruning this tree to give statistical reliability, and processing the pruned tree to improve understandability. This paper concerns the second stage—pruning. It presents empirical comparisons of the five methods across several domains. The results show that three methods—critical value, error complexity and reduced error—perform well, while the other two may cause problems. They also show that there is no significant interaction between the creation and pruning methods.

635 citations


Journal ArticleDOI
TL;DR: The paper considers a number of different measures and experimentally examines their behavior in four domains and shows that the choice of measure affects the size of a tree but not its accuracy, which remains the same even when attributes are selected randomly.
Abstract: One approach to induction is to develop a decision tree from a set of examples. When used with noisy rather than deterministic data, the method involves three main stages – creating a complete tree able to classify all the examples, pruning this tree to give statistical reliability, and processing the pruned tree to improve understandability. This paper is concerned with the first stage – tree creation – which relies on a measure for “goodness of split,” that is, how well the attributes discriminate between classes. Some problems encountered at this stage are missing data and multi-valued attributes. The paper considers a number of different measures and experimentally examines their behavior in four domains. The results show that the choice of measure affects the size of a tree but not its accuracy, which remains the same even when attributes are selected randomly.

502 citations


Journal ArticleDOI
TL;DR: An algorithm for distributed mutual exclusion in a computer network of N nodes that communicate by messages rather than shared memory that does not require sequence numbers as it operates correctly despite message overtaking is presented.
Abstract: We present an algorithm for distributed mutual exclusion in a computer network of N nodes that communicate by messages rather than shared memory. The algorithm uses a spanning tree of the computer network, and the number of messages exchanged per critical section depends on the topology of this tree. However, typically the number of messages exchanged is O(log N) under light demand, and reduces to approximately four messages under saturated demand.Each node holds information only about its immediate neighbors in the spanning tree rather than information about all nodes, and failed nodes can recover necessary information from their neighbors. The algorithm does not require sequence numbers as it operates correctly despite message overtaking.

473 citations


Journal ArticleDOI
TL;DR: Algorithms are presented for automatically constructing a binary decision tree designed to estimate the probability that a given word will be the next word uttered, which is compared to an equivalent trigram model and shown to be superior.
Abstract: The problem of predicting the next word a speaker will say, given the words already spoken; is discussed. Specifically, the problem is to estimate the probability that a given word will be the next word uttered. Algorithms are presented for automatically constructing a binary decision tree designed to estimate these probabilities. At each node of the tree there is a yes/no question relating to the words already spoken, and at each leaf there is a probability distribution over the allowable vocabulary. Ideally, these nodal questions can take the form of arbitrarily complex Boolean expressions, but computationally cheaper alternatives are also discussed. Some results obtained on a 5000-word vocabulary with a tree designed to predict the next word spoken from the preceding 20 words are included. The tree is compared to an equivalent trigram model and shown to be superior. >

444 citations


Proceedings Article
20 Aug 1989
TL;DR: In this paper, a graph representation of the domain model is interactively created by using instances of the basic network components, nodes and arcs, as building blocks, together with the quantitative relations between nodes and their immediate causes expressed as conditional probabilities, are automatically transformed into a tree structure.
Abstract: Causal probabilistic networks have proved to be a useful knowledge representation tool for modelling domains where causal relations in a broad sense are a natural way of relating domain objects and where uncertainty is inherited in these relations. This paper outlines an implementation the HUGIN shell - for handling a domain model expressed by a causal probabilistic network. The only topological restriction imposed on the network is that, it must not contain any directed loops. The approach is illustrated step by step by solving a genetic breeding problem. A graph representation of the domain model is interactively created by using instances of the basic network components-- nodes and arcs--as building blocks. This structure, together with the quantitative relations between nodes and their immediate causes expressed as conditional probabilities, are automatically transformed into a tree structure, a junction tree. Here a computationally efficient and conceptually simple algebra of Bayesian belief universes supports incorporation of new evidence, propagation of information, and calculation of revised beliefs in the states of the nodes in the network. Finally, as an exam ple of a real world application, MUNIN an expert system for electromyography is discussed.

398 citations


Book ChapterDOI
01 Jan 1989

287 citations


01 Jan 1989

263 citations


Book ChapterDOI
05 Nov 1989
TL;DR: In this paper, a reduced-order approximation for the Taylor series expansion coefficients of the driving-point admittance of an RC tree is presented. But this algorithm is not suitable for the case of series resistance.
Abstract: An efficient algorithm is presented which accounts for series resistance by computing a reduced-order approximation for the driving-point admittance of an RC tree. The algorithm consists of four rules which allow the Taylor series expansion coefficients of the driving-point admittance looking downstream of a given point in the tree to be correctly propagated further upstream. Rules 1-3 involve movement upstream, along a single branch, and past, respectively, a lumped capacitor to ground, a series lumped resistor, and a uniformly distributed RC segment. Rule 4 involves combining two or more different admittance expansions in parallel at a branch point in the tree. Using an emitter-coupled-logic clock buffer as an example, the authors demonstrate a significant improvement in accuracy. >

252 citations


Journal ArticleDOI
TL;DR: Results indicate that the history heuristic combined with transposition tables significantly outperforms other alpha-beta enhancements in application-generated game trees.
Abstract: Many enhancements to the alpha-beta algorithm have been proposed to help reduce the size of minimax trees. A recent enhancement, the history heuristic, which improves the order in which branches are considered at interior nodes is described. A comprehensive set of experiments is reported which tries all combinations of enhancements to determine which one yields the best performance. In contrast, previous work on assessing their performance has concentrated on the benefits of individual enhancements or a few combinations. The aim is to find the combination that provides the greatest reduction in tree size. Results indicate that the history heuristic combined with transposition tables significantly outperforms other alpha-beta enhancements in application-generated game trees. For trees up to depth 8, this combination accounts for 99% of the possible reductions in tree size, with the other enhancements yielding insignificant gains. >

249 citations


Patent
Philip A. Chou1
31 Oct 1989
TL;DR: In this article, a method of automatically identifying bitmapped image objects is presented, where each of a set of templates in an object template library is compared with all areas of like size of a bit mapped image and the set of signals generated for each such comparison that satisfies a defined matching criteria between the template and the image area being compared.
Abstract: A method of automatically identifying bitmapped image objects. Each of a set of templates in an object template library is compared with all areas of like size of a bitmapped image. A set of signals is generated for each such comparison that satisfies a defined matching criteria between the template and the image area being compared. The set of signals identifies the object based on the matching template, the location of the object in the image and an indication of the goodness of the match between the object and the template. A series of possible parse trees are formed that describe the image with a probability of occurrence for each tree. Each parent node and its child nodes of each parse tree satisfies a grammatical production rule in which some of the production rules define spatial relationships between objects in the image. The one of the possible parse trees which has the largest probability of occurence is selected for further utilization.

Proceedings Article
01 Jul 1989
TL;DR: The paging algorithm for the binary tree directory is interesting in its own right because a practical solution for the problem of how to page a (multidimensional)b inary tree without access to degeneration is presented.
Abstract: We propose the Local Split Decision tree (LSD tree, for short), a data structure supporting efficient spatial access to geometrico bjects.I ts main advantageosv er other structures are that it performsw ell for all reasonabled atad istributions, cover quotients( which measureth e overlappingo f the data objects), and bucket capacities, and that it maintains multidimensional points as well as arbitrary geometric objects. Thesep ropertiesd emonstratedb y an extensivep erformance,evaluation make the LSD tree extremely suitable for the implementationo f spatiala ccessp athsi n geometricd atabases. The paging algorithm for the binary tree directory is interesting in its own right because a practical solution for the problem of how to page a (multidimensional)b inary tree without accessp ath degenerationis presented.

Journal ArticleDOI
TL;DR: The paper presents a case study in examining the bias of two particular formalisms: decision trees and linear threshold units, and produces a new hybrid representation, called a perceptron tree, and an associated learning algorithm called the perceptronTree error correction procedure.
Abstract: This article presents a case study in examining the bias of two particular formalisms: decision trees and linear threshold units. The immediate result is a new hybrid representation, called a ‘perceptron tree’, and an associated learning algorithm called the ‘percepton tree error correction procedure’. The longer term result is a model for exploring issues related to understanding representational bias and constructing other useful hybrid representations.

Journal ArticleDOI
TL;DR: Simulation results demonstrate the recursive partitioning algorithm's capability to identify the underlying hazard structure in survival data and its integration into a computer program similar in structure to the commercial package CART.
Abstract: This paper concerns a recursive partitioning algorithm for incomplete survival data. The splitting criterion employed is exponential log-likelihood loss. The method has been integrated into a computer program similar in structure to the commercial package CART. Special features incorporated into the program include a modification to prevent zero hazard estimates during the the cross-validation procedure and a method based on the chi-square distribution for final tree selection. Simulation results demonstrate the program's capability to identify the underlying hazard structure in survival data. An example utilizing data from patients with diffuse large cell lymphoma is presented.

Journal ArticleDOI
TL;DR: This work describes strategies for weighting the data that circumvent some of the problems of dependency in an evolutionary tree.

Proceedings ArticleDOI
14 Nov 1989
TL;DR: Numerical results on a waveform recognition problem are presented to support the theory and practical considerations suggest that the iterative tree growing and pruning algorithm should perform better and require less computation than other widely used tree grow and prune algorithms.
Abstract: An efficient iterative method is proposed to grow and prune classification trees. This method divides the data sample into two subsets and iteratively grows a tree with one subset and prunes it with the other subset, successively interchanging the roles of the two subsets. The convergence and other properties of the algorithm are established. Theoretical and practical considerations suggest that the iterative tree growing and pruning algorithm should perform better and require less computation than other widely used tree growing and pruning algorithms. Numerical results on a waveform recognition problem are presented to support this view. >

Journal ArticleDOI
TL;DR: Monte Carlo experiments are described which illustrate the effectiveness of the ·632 bootstrap as an alternative technique for tree selection and error estimation and a new incremental learning extension to CART is described.
Abstract: The CART concept induction algorithm recursively partitions the measurement space, displaying the resulting partitions as decision trees. Care, however, must be taken not to overfit the trees to the data, and CART employs cross-validation (cv) as the means by which an appropriately sized tree is selected. Although unbiased, cv estimates exhibit high variance, a troublesome characteristic, particularly for small learning sets. This paper describes Monte Carlo experiments which illustrate the effectiveness of the ·632 bootstrap as an alternative technique for tree selection and error estimation. In addition, a new incremental learning extension to CART is described.

Proceedings ArticleDOI
06 Feb 1989
TL;DR: The design of the cell tree, an object-oriented dynamic index structure for geometric databases, is described, which is designed for paged secondary memory to minimize the number of disk accesses occurring during a tree search.
Abstract: The design of the cell tree, an object-oriented dynamic index structure for geometric databases, is described. The data objects in the database are represented as unions of convex point sets (cells). The cell tree is a balanced tree structure whose leaves contain the cells and whose interior nodes correspond to a hierarchy of nested convex polyhedra. This index structure allows quick access to the cells (and thereby to the data objects) that occupy a given location in space. The cell tree is designed for paged secondary memory to minimize the number of disk accesses occurring during a tree search. Point locations and range searches can be carried out very efficiently using the cell tree. >

Journal ArticleDOI
TL;DR: The Dobkin-Lipton result raised the question of whether an O(log n ) bound on query time can be achieved using only O(n) space, which is optimal if the planar subdivision must be stored, and showed that this lower bound is tight.
Abstract: A classical problem in computational geometry is the planar point location problem. This problem calls for preprocessing a polygonal subdivision of the plane defined by n line segments so that, given a sequence of points, the polygon containing each point can be determined quickly on-line. Several ways of solving this problem in O(log n) query time and O(n) space are known, but they are all rather complicated. We propose a simple O(log n)-query-time, O(n)-space solution, using persistent search trees. A persistent search tree differs from an ordinary search tree in that after an insertion or deletion, the old version of the tree can still be accessed. We develop a persistent form of binary search tree that supports insertions and deletions in the present and queries in the past. The time per query or update is O(log m), where m is the total number of updates, and the space needed is O(1) per update. Our planar point location algorithm is an immediate application of this data structure. The structure also provides an alternative to Chazelle's "hive graph" structure, which has a variety of applications in geometric retrieval.

Journal ArticleDOI
TL;DR: The authors explore the connection between CAGD (computer-aided geometric design) and computer vision by using a novel technique to quantify the properties of features which compose models used in computer vision: robustness, completeness, consistency, cost, and uniqueness.
Abstract: The authors explore the connection between CAGD (computer-aided geometric design) and computer vision. A method for the automatic generation of recognition strategies based on the 3-D geometric properties of shape has been devised and implemented. It uses a novel technique to quantify the following properties of features which compose models used in computer vision: robustness, completeness, consistency, cost, and uniqueness. By utilizing this information, the automatic synthesis of a specialized recognition scheme, called a strategy tree, is accomplished. Strategy trees describe, in a systematic and robust manner, the search process used for recognition and localization of particular objects in the given scene. The consist of selected 3-D features which satisfy system constraints and corroborating evidence subtrees which are used in the formation of hypotheses. Verification techniques, used to substantiate or refute these hypotheses are explored. Experiments utilizing 3-D data are presented. >

Journal ArticleDOI
Robert E. Wilber1
TL;DR: It can be proven that the bit-reversal permutation requires $\Theta (n\log n)$ time to access in this model, and it is shown that the expected cost of accessing random sequences in thismodel is the same as it is for the case where the tree is static.
Abstract: Two methods are given for obtaining lower bounds on the cost of accessing a sequence of nodes in a symmetrically ordered binary search tree, in a model where rotations can be done on the tree and the entire sequence is known before accessing begins (but the accesses must be done in the order given). For example, it can be proven that the bit-reversal permutation requires $\Theta (n\log n)$ time to access in this model. It is also shown that the expected cost of accessing random sequences in this model is the same as it is for the case where the tree is static.

Proceedings ArticleDOI
Michael Riley1
15 Oct 1989
TL;DR: Several applications of statistical tree-based modelling are described in this paper, including automatic stop classification, segment duration prediction for synthesis, phoneme-to-phone classification, and end-of-sentence detection in text.
Abstract: Several applications of statistical tree-based modelling are described here to problems in speech and language. Classification and regression trees are well suited to many of the pattern recognition problems encountered in this area since they (1) statistically select the most significant features involved (2) provide "honest" estimates of their performance, (3) permit both categorical and continuous features to be considered, and (4) allow human interpretation and exploration of their result. First the method is summarized, then its application to automatic stop classification, segment duration prediction for synthesis, phoneme-to-phone classification, and end-of-sentence detection in text are described. For other applications to speech and language, see [Lucassen 1984], [Bahl, et al 1987].

Journal ArticleDOI
TL;DR: This paper presents a branch-and-bound algorithm for the exact solution of the Tree QAP based on an integer programming formulation of the problem and the bounds are computed using a Lagrangian relaxation of this formulation.
Abstract: The Tree QAP is a special case of the Quadratic Assignment Problem QAP where the nonzero flows form a tree. No condition is required for the distance matrix. This problem is NP-complete and is also a generalization of the Traveling Salesman Problem. In this paper, we present a branch-and-bound algorithm for the exact solution of the Tree QAP based on an integer programming formulation of the problem. The bounds are computed using a Lagrangian relaxation of this formulation. To solve the relaxed problem, we present a Dynamic Programming algorithm which is polynomially bounded. The obtained lower bound is very sharp and equals the optimum in many cases. This fact allows us to employ a reduction method to decrease the number of variables and leads to search-trees with a small number of nodes compared to those usually encountered in problems of this type. Computational results are given for problems with size up to 25.

Patent
28 Sep 1989
TL;DR: A prefix index tree as discussed by the authors is a tree structure for locating data records stored through keys related to information stored in data records, where each node includes a prefix field for a prefix string of length p of the longest string of key characters shared by all subtrees of the node.
Abstract: A prefix index tree structure for locating data records stored through keys related to information stored in data records. Each node includes a prefix field for a prefix string of length p of the longest string of key characters shared by all subtrees of the node and a data record field for a reference to a data record whose key is completed by the prefix string. A node may include one or more branch fields when the prefix string is a prefix of keys stored in at least one subtree of the node, with a branch field for each distinct p+1 st key character in the keys, wherein each p+1 st key character is a branch character. Each branch field includes a branch character and a branch pointer field for a reference to a node containing at least one key whose p+1 st character is the branch character. Each node further includes a field for storing the number of key characters in the prefix string and a field for storing the number of branch fields in the node. Also disclosed are methods for constructing and searching a prefix index tree of the present invention, and for inserting nodes into the tree and deleting nodes from the tree.



Journal ArticleDOI
TL;DR: In this article, column generation is used during the tree search procedure, combined with a ranking procedure which ensures that the exact optimal integer solution is obtained for the matrix decomposition problem in the context of satellite communication system optimization.

Journal ArticleDOI
TL;DR: It is shown that if the processing times of the tasks are not less that the data communication times between the tasks, the associated scheduling problem under tree-like precedence constraints is polynomial and an efficient algorithm is provided to solve it.