Showing papers on "Tree (data structure) published in 1974"

Quad trees a data structure for retrieval on composite keys

Abstract: The quad tree is a data structure appropriate for storing information to be retrieved on composite keys. We discuss the specific case of two-dimensional retrieval, although the structure is easily generalised to arbitrary dimensions. Algorithms are given both for staightforward insertion and for a type of balanced insertion into quad trees. Empirical analyses show that the average time for insertion is logarithmic with the tree size. An algorithm for retrieval within regions is presented along with data from empirical studies which imply that searching is reasonably efficient. We define an optimized tree and present an algorithm to accomplish optimization in n log n time. Searching is guaranteed to be fast in optimized trees. Remaining problems include those of deletion from quad trees and merging of quad trees, which seem to be inherently difficult operations.

Adjacency in digital pictures

Abstract: Let S be a subset of a digital picture, and let s be the complement of S. It is well known that the connected components of S and s, under the relation “is adjacent to,≓ form a tree, and algorithms for constructing this tree have been devised. The main purpose of this paper is to prove that the components do form a tree, and in the process, to provide a basis for proving the validity of the tree-constructing algorithms.

Augmented Threaded Index Method For Network Optimization

Abstract: Easily manipulated list structures for recording the basis tree for adjacent extreme point (“simplex type”) network algorithms are paramount to the development of computationally efficient network ...

Cutting down recursive trees

Abstract: A recursive tree is constructed by starting with a source node and repeatedly adjoining new nodes to one node of the tree already constructed. Such a tree could represent, for example, the spread of contamination from a single source within some organism. If we remove an edge from such a tree it falls into two subtrees one of which contains the source. If we continue to remove edges from the successively smaller subtrees that contain the source we eventually isolate the source. We consider how many randomly selected edges must be removed on the average before isolating the source by this procedure.

A Minimax Location Problem on a Network

Abstract: We consider a network model of a system of transportation links, with nodes representing locations of existing facilities, and study the problem of finding a new facility location on the network that minimizes the maximum of linear increasing functions of the “network distances” between the new facility and the existing facilities. The problem is formulated with respect to a metric space which is defined on the network, and a number of properties of the problem are developed. The properties lead to a new, simple algorithm for solving the problem when the network is a tree, and to a new, equivalent spanning tree problem for a general network.

Tree climbing device

Abstract: A pair of projecting platforms attached around a tree trunk one above the other are moved up a tree by a person sitting on the uppermost platform and reaching below and pulling the lowermost platform up close to the botton of the uppermost platform and then while standing on the lowermost platform rising from the seat of the uppermost platform and lifting it upwardly behind and then repeating the procedure until the desired height is reached. The uppermost and lowermost platforms both have adjustable tree-engaging frames which are placed around the tree trunk.

Tree encoding of Gaussian sources

Abstract: Tree codes are known to be capable of performing arbitrarily close to the rate-distortion function for any memoryless source and single-letter fidelity criterion. Tree coding and tree search strategies are investigated for the discrete-time memoryless Gaussian source encoded for a signal-power-to-mean-squared-error ratio of about 30 dB (about 5 binary digits per source output). Also, a theoretical lower bound on average search effort is derived. Two code search strategies (the Viterbi algorithm and the stack algorithm) were simulated in assembly language on a large digital computer. After suitable modifications, both strategies yielded encoding with a signal-to-distortion ratio about 1 dB below the limit set by the rate-distortion function. Although this performance is better than that of any previously known instrumentable scheme, it unfortunately requires search computation of the order of l0^5 machine cycles per source output encoded.

A branch search algorithm for maximum likelihood paired comparison ranking

Abstract: SUMMARY An efficient algorithm is presented for solving a general class of mathematical programmning problems. This class ineludes the specific task of finding a maximum likelihood ranking based on paired comparison data. It differs from a branch and bound scheme in that it searches the nodes of a tree one branch at a time. As a result, its time requirements appear to be better and its storage requirements are better than or as good as previous algorithms. An example from the literature is presented for illustration and comparison of this method with previous work. Computational experience is described for an important class of problems.

Tree Distribution on Perennially Frozen Earth Hummocks

Abstract: Earth hummocks occur on vast areas of trees in the mature forests lean away from the perennially frozen mineral soils in the western hummocks as a result of severe and repeated Canadian subarctic regions. Different vegetation ground heaving. The internal structure of humgrows on different parts of the hummocks. The mocks suggests periodic movements of soil by tops of the hummocks are vegetated by plants cryoturbation, and the absence of trees on that have no roots (lichens, mosses) or by hummock tops is attributed to the same process short-lived plants. Trees seldom grow on humand to somewhat droughty conditions caused mock tops, occurring mainly on the sides of by the pronounced microrelief. hummocks or in interhummock troughs. Most

Tree harvesting apparatus

Abstract: A tree accumulator mechanism for collecting a plurality of trees on a rigid support forming part of a tree harvesting apparatus is disclosed herein. The accumulator means consists of a compound linkage that is interposed between the rigid support and a movable arm that forms part of the tree grapple means for supporting a tree while it is being severed by tree cutting means. The linkage is arranged so that one link defines an arm for accumulating a plurality of trees relative to fixed tree engaging elements.

Reliability Calculations with a List Processing Technique

Abstract: The implementation of list processing techniques for the evaluation of the reliability of large systems represented by fault trees is described. Using advanced methods from tree theory, an endorder traversal of the oriented input tree is rapidly pruned by identifying known patterns and replacing corresponding branches by leaves. A computer code has been written to demonstrate these techniques.

Tree and stump extraction

Abstract: A method and apparatus are provided for recovering stump and root systems in timber harvesting by exerting a vertical lifting force combined with simultaneously vibrating the trunk of a tree or stump being harvested.

Staking landscape trees

Abstract: This paper suggests different staking techniques for providing, where necessary, adequate flexible support for trees in windy situations and reasonable protection with little or no tree injury. Reasons for supporting and protecting the tree with staking include protecting the trunk from damage by equipment, vehicles, and vandals; anchoring the root system; and supporting the trunk in an upright position. A young tree standing alone with its top free to move usually becomes a strong tree better able to withstand the elements. When support is essential, make the stakes as short as possible, but high enough to hold the tree upright under calm conditions; the tree should return to vertical after the wind has bent the top.

The Tree of Knowledge and the Law of Yahweh

Abstract: The terminology used to describe the law of Yahweh in Ps. xix 8 ff. is reminiscent of the description of the tree of knowledge of good and evil (Gen. ii 9, 17; iii 5 ff.). It is here suggested that the author of Ps. xixB intended by his allusions to Gen. ii-iii to assert the superiority of the law to the tree of knowledge as a means of obtaining wisdom. The terms of interest are principally the five two-word phrases which form the second halves of the five stichoi vv. 8-10a:

A study of order transformations of hierarchical structures in IMS data bases

Abstract: Hierarchical structures are widely used in information processing. An application program written to traverse a hierarchical structure will not work properly, if at all, when the order of the structure (in the sense of tree order) is altered. This paper presents a method in the context of IMS systems to intercept and interpret data base manipulation commands issued by the application program to eliminate the necessity of reprogramming when a hierarchical structure is subject to an order transformation. Algorithms involving command substitution rules for various situations have been derived to insure the correct execution of application programs irrespective of the order of the structure.

Disposable Christmas tree stand

Abstract: A disposable Christmas tree stand consisting of three separate, substantially identical bracket members each formed from highstrength steel wire and adapted to be secured to and cooperate with the base of a Christmas tree to provide a highly stable support for the tree with the base of the tree spaced above the floor The bracket members provide maximum support against twisting or turning movement of the tree, and are shaped to permit the base of a tree to be positioned in an open container of water on the floor to prolong the life of the tree