Showing papers on "Tree (data structure) published in 1979"

Tree algorithms for packet broadcast channels

Abstract: The multiaccessing of a broadcast communication channel by independent sources is considered. Previous accessing techniques suffer from long message delays, low throughput, and/or congestion instabilities. A new class of high-speed, high-throughput, stable, multiaccessing algorithms is presented. Contentions resolving tree algorithms are introduced, and they are analyzed for specific probabilistic source models. It is shown that these algorithms are stable (in that all moments of delay exist) and are optimal in a certain sense. Furthermore, they have a maximum throughput of 0.430 packets/slut and have good delay properties. It is also shown that, under heavy traffic, the optimally controlled tree algorithm adaptively changes to the conventional time-division multiple access protocol.

Flow analysis and optimization of LISP-like structures

Abstract: In [12] the authors introduced the concept of binding time optimization and presented a series of data flow analytic methods for determining some of the binding time characteristics of programs. In this paper we extend that work by providing methods for determining the class of shapes which an unbounded data object may assume during execution of a LISP-like program, and describe a number of uses to which that information may be put to improve storage allocation in compilers and interpreters for advanced programming languages.We are concerned chiefly with finding, for each program point and variable a finite description of a set of graphs which includes all the shapes of values the variable could assume at that point during the execution of a program. If this set is small or regular in structure, this information can be used to optimize the program's execution, mainly by use of more efficient storage allocation schemes.In the first part we show how to construct from a program without selective updating a tree grammar whose nonterminals generate the desired sets of graphs; in this case they will all be trees. The tree grammars are of a more general form than is usually studied [8, 19], so we show that they may be converted to the usual form. The resulting tree grammar could naturally be viewed as a recursive type definition [11] of the values the variables may assume. Further, standard algorithms may be employed to test for infiniteness, emptiness or linearity of the tree structure.In the second part selective updating is allowed, so an alternate semantics is introduced which more closely resembles traditional LISP implementations, and which is equivalent to the tree model for programs without selective updating. In this model data objects are directed graphs. We devise a finite approximation method which provides enough information to detect cell sharing and cyclic structures whenever they can possibly occur. This information can be used to recognize when the use of garbage collection or of reference counts may be avoided.The work reported in the second part of this paper extends that of Schwartz [17] and Cousot and Cousot [7]. They have developed methods for determining whether the values of two or more variables share cells, while we provide information on the detailed structure of what is shared. The ability to detect cycles is also new. It also extends the work of Kaplan [13], who distinguishes only binary relations among the variables of a program, does not handle cycles, and does not distinguish selectors (so that his analysis applies to nodes representing sets rather than ordered tuples).

Chemical graphs: XXXIV. Five new topological indices for the branching of tree-like graphs [1]

Abstract: In order to find the centre of an acyclic connected graph (of a tree), vertices of degree one (endpoints) are removed stepwise. The numbers δi of vertices thus removed at each step form a digit sequenceS (pruning sequence) which reflects the branching of the tree. The sum of squares of digits in the sequenceS affords a new topologicalcentric index B = ∑i δi2 for the branching of trees. Comparisons with other topological indices are presented evidencing thatB induces an ordering of isomeric trees distinct from those induced by all other indices devised so far, becauseB emphasizes equally branches of similar length.It is shown that Rouvray's indexIis equivalent to Wiener's indexw, and that the Gordon-Scantlebury indexN2 and Gutmanet al.'s indexM1 belong to the same family, calledquadratic indices, and induce the same ordering.Since all topological indices vary both with the branching and the number of vertices in the tree, four new indices are devised fromB andM1 to account only (or mainly) for the branching, by normalization (imposing a lower bound equal to zero for chain-graphs, i.e.n-alkanes) or binormalization (same lower bound, and upper bound equal to one for star-graphs). Normalized and binormalized centric (C, C′) and quadratic indices (Q, Q′) are presented for the lower alkanes. From the five new topological indices, the centric indices (B, C, C′) are limited to trees, but the quadratic indices (Q, Q′) apply to any graph. Binormalized indices (C′,Q′) express the “topological shape” of the graph.

Tree -ring skeleton plotting by computer

Abstract: Skeleton plotting is an established manual technique for representing the relative narrowness of tree rings in a single radius. These plots can be used as a visual aid to crossdating. This paper describes a method for deriving these plots by computer. The method uses a low -pass digital filter, running means, and standard deviations of ring

A Tree-to-Tree Distance and Its Application to Cluster Analysis

Abstract: A distance measure between two trees is proposed. Using the idea of language transformation, a tree can be derived from another by a series of transformations. The distance between the two trees is the minimum-cost sequence of transformations. Based on this definition, an algorithm that generates the distance for any two trees is presented. Cluster analysis for patterns represented by tree structures is discussed. Using a tree-to-tree distance, the similarity between patterns is measured in terms of distance between their tree representations. An illustrative example on clustering of character patterns is presented.

Tree Design: Some Biological Solutions to Mechanical Problems

Abstract: An engineer might look at a tree as a tower (the stem and branches) supporting many small solar collectors (the leaves). From a design standpoint, the tower is an open network of cantilever beams (Fig. 1). These beams must be designed so they will not break in storms, but structural materials must be used efficiently because their cost is high. The arrangement of the beams should display the solar collectors to maximize the total

Increasing tree search efficiency for constraint satisfaction problems

Abstract: In this paper we explore the number of consistency checks made by a tree search in order to solve binary constraint satisfaction problems. We show analytically and experimentally that the two principles of first trying the places most likely to fail and remembering what has been done to avoid repeating the same mistake twice improve the standard backtracking search. We experimentally show that a lookahead procedure called forward checking (to remember the future) which employs the most likely to fail principle performs better than standard backtracking, Ullman's, Waltz's, Mackworth's, and Haralick's discrete relaxation in all cases tested, and better than Gaschnigs backmarking in the larger problems.

Performance and comparison of stand growth models based on individual tree and diameter class growth

Abstract: A distance-dependent individual tree based growth model (FOREST) was compared with a diameter-class growth model (SHAF) for describing changes in stand density and structure. Projections of Lake St...

Adaptation Algorithms for Binary Tree Networks

Abstract: The automatic synthesis of Boolean switching functions by adaptive tree networks is discussed. The concept of heuristic responsibility, by means of which parts of a tree become specialized to certain subsets of input vectors, is explained. Applications to pattern recognition and optical character recognition (OCR) problems are described.

Computing Perimeters of Images Represented by Quadtrees

Abstract: : An algorithm is presented for computing the total perimeter of a binary image represented by a quadtree. The algorithm explores each segment of the border once and only once. Analysis of the algorithm shows that its worst- case average execution time is proportional to the product of the log of the image diameter and the number of nodes in the tree.

A Theory of Water Tree Initiation and Growth

Abstract: Treeing may be roughly divided into two major stages: the initiation which involves the formation of the first tiny tree branch and its further growth to a tree. The possibility of tree growth is first discussed under the assumption that the initiation has taken place and thereafter the possible mechanisms by which the tree initiation may take place are considered.

Interrupted Point Processes

Abstract: A simple random thinning procedure for point processes is considered. The model is used for the description of a pattern generated by positions of tree seedlings.