Showing papers on "Tree (data structure) published in 1987"

The R+-Tree: A Dynamic Index for Multi-Dimensional Objects

Abstract: The problem of indexing multidimensional objects is considered. First, a classification of existing methods is given along with a discussion of the major issues involved in multidimensional data indexing. Second, a variation to Guttman’s Rtrees (R+-trees) that avoids overlapping rectangles in intermediate nodes of the tree is introduced. Algorithms for searching, updating, initial packing and reorganization of the structure are discussed in detail. Finally, we provide analytical results indicating that R+-trees achieve up to 50% savings in disk accesses compared to an R-tree when searching files of thousands of rectangles.

Tree Death as an Ecological Process

Abstract: the patterns and causes of tree death typically are complex, and we are only beginning to appreciate the complexities. Understanding and predicting tree mortality is critical in both applied and basic ecology. Practically speaking, information on mortality is essential in calculating forest stand yields and allocating efforts in tending and protecting forests. A thorough knowledge of tree death is also necessary to interpret correctly the dying back of forests. Yet, despite its long history, forest husbandry lacks a comprehensive understanding of tree mortality. In basic ecology, tree death is relevant to a broad array of topics. Ecolo-

Reconstructing ancestral character states under Wagner parsimony

Abstract: The problem of assigning optimal character states to the hypothetical ancestors of an evolutionary tree under the Wagner parsimony criterion is examined. A proof is provided for the correctness of Farris's well-known, but previously unproven, algorithm for solving this problem. However, the solution is not, in general, unique, and Farris's method obtains only a subset (generally only one) of the possible solutions. Algorithms that discover other solutions and that resolve ambiguities through the imposition of ancillary criteria are developed and discussed. A method for determining the optimal length of a given tree without actually assigning character states to hypothetical ancestors is described.

Generating production rules from decision trees

Abstract: Many inductive knowledge acquisition algorithms generate classifiers in the form of decision trees. This paper describes a technique for transforming such trees to small sets of production rules, a common formalism for expressing knowledge in expert systems. The method makes use of the training set of cases from which the decision tree was generated, first to generalize and assess the reliability of individual rules extracted from the tree, and subsequently to refine the collection of rules as a whole. The final set of production rules is usually both simpler than the decision tree from which it was obtained, and more accurate when classifying unseen cases. Transformation to production rules also provides a way of combining different decision trees for the same classification domain.

A Review of Hierarchical Classification

Abstract: SUMMARY A review is presented of methods of summarizing the relationships within a set of objects by a set of hierarchically-nested classes of similar objects, representable by a rooted tree diagram. Material covered includes algorithms for obtaining tree diagrams, comments on the selection of appropriate methods of analysis and the validation of classifications, distributions of different types of tree, and consensus trees.

Performance characteristics of tree codes

Abstract: Implantation FORTRAN de l'algorithme en arbre hierarchique de Barnes-Hut. Analyse dans le contexte du probleme astrophysique a N corps

DIB—a distributed implementation of backtracking

Abstract: DIB is a general-purpose package that allows a wide range of applications such as recursive backtrack, branch and bound, and alpha-beta search to be implemented on a multicomputer. It is very easy to use. The application program needs to specify only the root of the recursion tree, the computation to be performed at each node, and how to generate children at each node. In addition, the application program may optionally specify how to synthesize values of tree nodes from their children's values and how to disseminate information (such as bounds) either globally or locally in the tree. DIB uses a distributed algorithm, transparent to the application programmer, that divides the problem into subproblems and dynamically allocates them to any number of (potentially nonhomogeneous) machines. This algorithm requires only minimal support from the distributed operating system. DIB can recover from failures of machines even if they are not detected. DIB currently runs on the Crystal multicomputer at the University of Wisconsin-Madison. Many applications have been implemented quite easily, including exhaustive traversal (N queens, knight's tour, negamax tree evaluation), branch and bound (traveling salesman) and alpha-beta search (the game of NIM). Speedup is excellent for exhaustive traversal and quite good for branch and bound.

ID: An Incremental ID3

Abstract: THIS PAPER DESCRIBES ID5, AN INCREMENTAL ALGORITHM THAT PRODUCES DECISION TREES SIMILAR TO THOSE BUILT BY QUINLAN''S ID3 THE PRINCIPAL BENEFIT OF ID5 IS THAT NEW TRAINING INSTANCES CAN BE PROCESSED BY REVISING THE DECISION TREE INSTEAD OF BUILDING A NEW TREE FROM SCRATCH ID3, ID4, AND ID5 ARE DESCRIBED IN DETAIL, COMPARED, AND CONTRASTED EXPERIMENTS ILLUSTRATE OBSERVED PERFORMANCE IN TERMS OF TRAINING EXPENSE AND CLASSIFI- CATION ACCURACY

Generating an interpretation tree from a CAD model for 3D-object recognition in bin-picking tasks

Abstract: This article describes a method to generate 3D-object recognition algorithms from a geometrical model for bin-picking tasks. Given a 3D solid model of an object, we first generate apparent shapes of an object under various viewer directions. Those apparent shapes are then classified into groups (representative attitudes) based on dominant visible faces and other features. Based on the grouping, recognition algorithms are generated in the form of an interpretation tree. The interpretation tree consists of two parts: the first part for classifying a target region in an image into one of the shape groups, and the second part for determining the precise attitude of the object within that group. We have developed a set of rules to find out what appropriate features are to be used in what order to generate an efficient and reliable interpretation tree. Features used in the interpretation tree include inertia of a region, relationship to the neighboring regions, position and orientation of edges, and extended Gaussian images. This method has been applied in a task for bin-picking objects that include both planar and cylindrical surfaces. As sensory data, we have used surface orientations from photometric stereo, depth from binocular stereo using oriented-region matching, and edges from an intensity image.

Tree-Based Broadcasting in Multihop Radio Networks

Abstract: This paper considers the issue of broadcasting protocols in multihop radio networks. The objective of a broadcasting protocol is to deliver the broadcasted message to all network nodes. To efficiently achieve this objective the broad- casting protocol in this paper utilizes two basic properties of the multihop radio network. One is the broadcast nature of the radio which allows every single trasmission to reach all nodes that are in line of sight and within range of the transmitting node. The other, spatial reuse of the radio channel, which due to the multihop nature of the network allows multiple simultaneous transmissions to be received correctly. The proposed protocol incorporates these properties to obtain a collision free forwarding of the broadcasted message on a tree. Centralized and distributed algorithms for the tree construction are presented. The obtained trees are unique in incorporating radio oriented time ordering as part of their definition. In this way multiple copies of one or more broadcasted messages can be transmitted simultaneously without collision, requiring only a small number of message transmissions. Consequently, the protocol not only guarantees that the broadcasted message reaches all network nodes in bounded time, but also ensures that the broadcasting activity will use only limited channel bandwidth and node memory. The proposed broadcast protocol thus possesses the advantages of TDM solutions while allowing the channel bandwidth to be shared, concurrently with the broadcast, with other transmission activities as dictated, for instance, by data link protocols. Some NP-completeness proofs are also given.

The recovery of causal poly-trees from statistical data

Abstract: Poly-trees are singly connected causal networks in which variables may arise from multiple causes. This paper develops a method of recovering poly-trees from empirically measured probability distributions of pairs of variables. The method guarantees that, if the measured distributions are generated by a causal process structured as a poly-tree then the topological structure of such tree can be recovered precisely and, in addition, the causal directionality of the branches can be determined up to the maximum extent possible. The method also pinpoints the minimum (if any) external semantics required to determine the causal relationships among the variables considered.

The node-weighted Steiner tree problem

Abstract: The general Node-Weighted Steiner Tree problem is an extension of the standard Steiner Tree problem by the addition of node-associated weights. This article analyzes a special case of that problem, where the set of nodes, which must be included in the solution tree, consists of a single node, and all node weights are negative. The special case is shown to be NP-Complete, its integer programming formulation is presented, and heuristic procedures are proposed. Using Lagrangian relaxation and subgradient optimization, tight lower bounds were derived and utilized by a branch and bound algorithm. The effectiveness of the developed procedures is demonstrated by a set of computational experiments.

A new distributed algorithm to find breadth first search trees

Abstract: A new distributed algorithm is presented for constructing breadth first search (BFS) trees. A BFS tree is a tree of shortest paths from a given root node to all other nodes of a network under the assumption of unit edge weights; such trees provide useful building blocks for a number of routing and control functions in communication networks. The order of communication complexity for the new algorithm is O(V^{1.6} + E) where V is the number of nodes and E the number of edges. For dense networks with E \geq V^{1.6} this order of complexity is optimum.

Estimating “tree” logit models

Abstract: The existence of the “tree” generalisation of the multinomial logit model, its consistency with theories of “rational” human behaviour, as well as the advantages offered in terms of more realistic modelling by this model form, have all been known for some time. Although a few studies have applied tree logit models, however, applications have been restricted by practical and theoretical difficulties in the estimation of these models, in particular with the sequential estimation that has normally been necessary. This paper presents a new estimation procedure, employing the maximum likelihood criterion, for the estimation of tree logit models. The procedure is based on a simple notation for the tree structure and is believed to be original. It offers the possibility of estimating simultaneously all the parameters of general tree logit structures, without restriction on the number of levels but allowing the user to impose constraints of parameter equality where required. Results are presented indicating both the usefulness of the method in deriving improved models, relative to the more familiar sequential estimations, and its practicality and speed of operation on main-frame, minicomputers and microcomputers.

Digital signature system and method based on a conventional encryption function

Abstract: A method of generating digital signatures for signing an infinitely expandable series of messages M i . An infinitely expandable tree of signature nodes is used, where each node can be used to sign a message. Each node is also used to sign up to k subnodes, where k is an integer greater than one. Each signature used, both for signing messages and for signing subnodes, is a one time signature, which in the preferred embodiment is based on a one-way function F. The function F is made public. To sign a message M i the signer selects a previously unused node (i.e., node i) from the signature tree. The message signing key at this node is then used to sign this message. The sequence of nodes from the root of the tree (i.e. node l) to node i is then used to verify that the message signature is correct and has not been tampered with. Furthermore, this process proves that the message has not been tampered with. Advantages of the invention include the infinite expandability of the signature tree, dependable verification of messages based on the use of secure one time signatures (e.g., which may be based on one way functions), the small amount of computation required to set up a signature tree, the small amount of storage required to maintain a tree, and the ability to implement the invention using high speed conventional encryption equipment and methods.

A numerical study of the air flow within and around a single tree

Abstract: A three-dimensional non-hydrostatic numerical model has been used to investigate the air flow and turbulence around a single tree.

Classification trees: a new discrimination tool

Abstract: Classification trees are discriminant models structured as dichtomous keys. A simple classification tree is presented and contrasted with a linear discriminant function. Classification trees have several advantages when compared with linear discriminant analysis. The method is robust with respect to outlier cases. It is nonparametric and can use nominal, ordinal, interval, and ratio scaled predictor variables. Cross-validation is used during tree development to prevent overrating the tree with too many predictor variables. Missing values are handled by using surrogate splits based on nonmissing predictor variables. Classification trees, like linear discriminant analysis, have potential prediction bias and therefore should be validated before being accepted.

A Tile-Expansion Router

Abstract: A router based on a tile-expansion algorithm and corner stitching data structure is presented. This program finds connections with a minimum number of jogs and it ensures that a possible solution will be found. Using a working tree, it allows an exhaustive and recursive search along all available areas for routing. The connections are made going back through the working tree until the starting terminal is reached. There are two Manhattan layers that the user can choose for each direction to implement connections; the router can be used to wire hierarchical blocks using a chip planning methodology. The program has been successfully tested on examples concerning different classes of problems.

Reconfigurable Tree Architectures Using Subtree Oriented Fault Tolerance

Abstract: An approach to the design of reconfigurable tree architectures is presented in which spare processors are allocated at the leaves The approach is unique in that spares are associated with subtrees and sharing of spares between these subtrees can occur The Subtree Oriented Fault Tolerance (SOFT) approach is more reliable than previous approaches capable of tolerating link and switch failures for both single-chip and multichip tree implementations while reducing redundancy in terms of both spare processors and links VLSI layout is O(n) for binary trees and is directly extensible to N-ary trees and fault tolerance through performance degradation

The Relevance of Tree Adjoining Grammar to Generation

Abstract: Grammatical formalisms can be viewed as neutral with respect to comprehension or generation, or they can be investigated from the point of view of their suitability for comprehension or generation. Tree Adjoining Grammars (TAG) is a formalism that factors recursion and dependencies in a special way, leading to a kind of locality and the possibility of incremental generation. We will examine the relevance of these properties from the point of view of sentence generation.

Method for concurrent record access, insertion, deletion and alteration using an index tree

Abstract: A method for fetching key record data in a group or record keys according to at least a portion of a key record through an index tree is provided. The index tree provides concurrent accesses of record keys by different transactions. The index tree includes a root node connected to at least one level of nodes, each node having a key record reference to one of more nodes in a next successive level and having bottom nodes that provide access to the key data. The method consists of the steps of (1) traversing across said nodes from said root node by using said key record portion until a bottom node is reached; (2) limiting all but read accesses to the node being traversed and a previously accessed node, to other concurrent transactions; (3) identifying said key record in said bottom node; (4) limiting all but read accesses to said key record; (5) removing all access limitations to traversed nodes; (6) fetching key record data; and (7) removing the access limitation to the key record after the record data has been fetched. Further, methods for inserting and deleting record keys are provided. Additionally, a method for changing the index tree structure while allowing concurrent accesses to take place is provided.

Method and product involving translation and execution of programs by automatic partitioning and data structure allocation

Abstract: A set of source program modules are translated into machine code blocks. The original or intermediate source code is processed into a program description tree (152) having program description parameters. This tree corresponds to a hierarchical set of data structure definitions (136, 138). The program description tree is then traversed to generate a program attribute tree (154) having program attribute parameters. The program attribute parameters (154) and certain machine attribute parameters (156) are operated on to produce a mapping strategy tree (158) having mapping parameters. The mapping strategy parameters and the program description tree are then operated on to produce a distribution of machine code blocks (148), assemblages of which correspond to distributed phases of the computation.

A conceptual framework for tree improvement programs

Abstract: Forest tree improvement programs have become quite complex and program strategies and intensities vary dramatically around the world. It is often necessary to examine the reasons for each activity separately in order to ascertain how all steps fit together in a strategy aimed at achieving genetic gain. This paper establishes a conceptual framework that explains the purposes of the various activities of tree improvement and allows complicated program strategies to be easily conveyed. This conceptual model, called the breeding cycle, stresses why, not how, each activity is conducted. The breeding cycle turns around one time for each generation of breeding and is composed of various types of plant populations. Each plant population serves a role in the tree improvement program and is created form a preceding population in the cycle by an activity of the breeder. Tree improvement concepts are explained and the roles of genetic test plantations are described in the context of the breeding cycle. This conceptual model is useful for foresters responsible for implementing tree improvement programs, for students and breeders trying to understand and compare divergent program strategies and for managers responsible for making investment decisions.

Simultaneous update of priority structures.

Abstract: To avoid centralized bottlenecks, data structures for multiple computer systems must be simultaneously updatable and yet must have some coherent and consistent state. This can be achieved through judicious partitioning of system data structures and control of access to them in such a manner that (1) either different processes operate upon disjoint segments of a given structure; or (2) processes operate upon the same datum object, in a controlled manner. Partitioning of data structures can be by structure or content. It can also occur at multiple times. In this paper we demonstrate content partitioning of a k-ary tree data structure at runtime, to realize a simultaneously updatable priority queue. The tree algorithms are then generalized to banyan data structures and shown to possess attractive properties of simultaneous update and throughput.