Showing papers on "Tree (data structure) published in 1972"

An Efficient Branch and Bound Algorithm for the Warehouse Location Problem

Abstract: This paper introduces an efficient branch and bound algorithm for a special class of mixed integer programming problems called the warehouse location problem. A set of branching decision rules is proposed for selecting warehouses to be constrained open and closed from any node of the branch and bound tree. These rules are tested for their efficiency in reducing computation times and storage requirements to reach optimal solutions. An improved method of solving the linear programming problems at the nodes which substantially reduces the computations is also introduced in this paper.

The Augmented Predecessor Index Method for Locating Stepping-Stone Paths and Assigning Dual Prices in Distribution Problems

Abstract: The augmented predecessor indexing method provides an efficient way to update the basis and cost evaluators in adjacent extreme point solution methods for transportation problems. The method extends the predecessor indexing method, which was designed to exploit an ancestry relation in the basis tree, by showing how to exploit a more elaborate “family relation,” commonly known as a binary tree representation in computer list processing. This representation, sometimes called the “triple-label method,” was first suggested for application to network optimization problems by Ellis Johnson, who examined its use in the context of maximal flow problems. The augmented predecessor indexing method shows how to take special advantage of this representation in the context of the transportation problem, elaborating Johnson's work by providing an efficient method for characterizing successive basis trees with minimal relabeling. Moreover, we show how this procedure can be applied to update the transportation cost evalua...

Tree Seedling Growth: Effects of Shaking

Abstract: ence in the productivity of the vegetation on the control plots. Odum et al. (2) observed comparable differences in productivity during old field succession, but these were attributable to previous fertilization and changes in the growth forms of the dominants, factors not adequately discussed by Hurd et al. We have also observed significant differences in the primary production of herbaceous communities among fields of different quality, but not among fields differing principally in age (3). These data suggest that site quality rather than age may have been the more important of the confounded variables in the experiment of Hurd et al. BUFORD HoI.T Biology Department, Brookhaven National Laboratory, Upton, New York 11973

Tree-Ring Research in Europe

Abstract: In the last ten years tree -ring analysis in Europe and its application has been extended considerably. By varied methods, a number of chronologies have been established for conifers and deciduous trees from different climatic regions that partly reach back to periods before the birth of Christ. The focus of dendrochronological research is usually dating and climatological studies are carried on only sporadically.

Probability sort in a storage minimized optimum processor

Abstract: A trainable signal processor having at least one input signal u and one desired output signal z applied thereto during training and having at least one actual output signal derived therefrom during execution is provided. From each member of the input sequence u(ti) a key Ki is generated. Ki may have only a finite number of values and is a single valued function of u. Corresponding to each value of the Ki generated during training, a trained response is derived from samples of the desired output signal z measured at those instances ti at which that value of Ki occurred. This operation is such that the contemporary value of the trained response is maintained in a tree allocated file. The file thereby associates with each key Ki a trained response. Storage is provided for only those Ki which actually occurred during training, which is an important attribute since these typically constitute a small fraction of those values which may theoretically occur, especially when the input is of multidimensional character. During execution the tree allocated file provides for efficient retrieval of the trained responses which are employed in determining the actual output signal of the processor. Whereas the tree allocation can greatly reduce the storage relative to that of the storage-wise inefficient method of direct addressing, the speed of operation is less due to the need to perform a sequence of operations on components of the key. Disclosed herein is a means of greatly improving the speed of the tree allocated file while retaining its advantages. The means involves control of the tree structure through a probability sorting operation which is effected periodically to arrange the nodes within the tree such that the modes of a filial set which are selected most frequently during training are placed near the entry node of the set. Specifically the node most likely to be selected is made the entry node of the set; it is chained to the node next most likely to be selected, etc., leaving the node least likely to be selected the terminal node of the set. This property holds for all sets of nodes within the tree.

Shoe tree with article basket

Abstract: An article basket attached to the toe section of a shoe tree by a suitable means which allows the basket to be folded into and removed from the cavity of the toe section. Complementary fastening means releasably locks the basket inside the toe section.

A Simple Network Capable of Inductive Generalization

Abstract: Various networks have been described which will function as content addressable memories; when given an incomplete description of a stored item they will supply those features of the item which are missing from the description. In this paper we consider a more difficult problem, that of designing a network which will also accept a description to which no stored item corresponds, and will supplement such a description by inductive generalization over the items already in store. This problem is tractable only if the ensemble of possible items is restricted in some way. A reasonable restriction is to assume ( i ) that any item can be fully described by a binary vector of fixed length, where the value of any component indicates the value of the corresponding binary feature; ( ii ) that no two features are logically independent of one another. Condition ( ii ) implies for example, that the ensemble does not contain items answering to all four of the descriptions + + ... , + — ..., — + ... and — .... If these conditions are satisfied, the ensemble may be represented as a tree, in which each node corresponds to a possible item and each link to the alteration of one or more features. A simple network is described, incorporating modifiable switches and threshold logic, which will supply all the inferences which could be drawn about an incompletely described item by inspecting this tree. It is possible, furthermore, to give a clear interpretation to the output of the network when the input describes an item which could not possibly belong to the same ensemble as those in store.

Tree moving apparatus

Abstract: A tree moving apparatus mounted on a vehicle and having a plurality of reciprocal blades arranged for positioning thereof around the trunk of a tree and spaced therefrom. The blades are substantially spoon-shaped and pierce the earth surrounding the tree at an angle with respect to the horizontal resulting in an arcuate configuration for the sidewalls of the area being excavated by the blades, and in such a manner as to meet beneath the tree in the form of a substantially semi-spherical container. The earth surrounding the tree is thus severed by the blades and the major roots of the tree are balled or encased within the closed container formed thereby. An inner frame bears against the exposed surface of the ground surrounding the tree and circumscribed by the blades for securely retaining the balled roots in the closed container. The container housing the tree and balled roots may then be elevated from the normal growing position of the tree and tilted to a substantially horizontal position whereupon the tree and contained roots may be transported to a new site for transplanting of the tree. A leveling device facilitates transplanting of the tree in a substantially true vertical position at the new site.