Showing papers on "Interval tree published in 1985"

An algorithm for distributed computation of a spanningtree in an extended LAN

Abstract: A protocol and algorithm are given in which bridges in an extended Local Area Network of arbitrary topology compute, in a distributed fashion, an acyclic spanning subset of the networkThe algorithm converges in time proportional to the diameter of the extended LAN, and requires a very small amount of memory per bridge, and communications bandwidth per LAN, independent of the total number of bridges or the total number of links in the networkAlgorhymeI think that I shall never see A graph more lovely than a treeA tree whose crucial property Is loop-free connectivityA tree which must be sure to span So packets can reach every LANFirst the Root must be selected By ID it is electedLeast cost paths from Root are traced In the tree these paths are placedA mesh is made by folks like me Then bridges find a spanning tree

Waveform Correlation by Tree Matching

Abstract: A waveform correlation scheme is presented. The scheme consists of four parts: 1) the representation of waveforms by trees, 2) the definition of basic operations on tree nodes and tree distance, 3) a tree matching algorithm, and 4) a backtracking procedure to find the best node-to-node correlation. This correlation scheme has been implemented. Results show that the scheme has the capability of handling distortions that result from stretching or shrinking of intervals or from missing intervals.

Generating binary trees using rotations

Abstract: A new algorithm that, for the first time, exploits the rotational geometry of binary trees is developed in order to allow for the lexicographic generation of computer representations of these trees in average time O(1) per tree. “Rotation” codewords for these trees (in average time O(1) per tree) are also generated. It is shown how these codewords relate to lattice paths, and, using this relationship, that n(n - 1)/(n + 2) is the average number of rotations needed to generate a binary tree on n nodes. Finally, a necessary and sufficient condition that a codeword represent a full binary tree (each node has 0 or 2 sons) on n = 2m + 1 nodes is given and how to contract this codeword to obtain the codeword for the binary tree on m nodes for which this full tree is the extended binary tree is shown.

A transform tree code for stationary Gaussian sources

Abstract: A new tree code is introduced for discrete-time stationary Gaussian sources with hounded, integrable power spectra and the squared-error distortion measure. The codewords in the tree are reconstructions of Karhunen-Loeve transforms of the source words. The branching factor and the number of code letters per branch may vary with level in the tree. A theorem that guarantees the existence of an optimal code for any code rate using such a tree is proved. The proof uses the random coding argument in conjunction with a theorem on survival of a branching process with random environment. A suboptimal but computationally affordable realization of the theorem's coding technique was used for encoding simulations for six autoregressive sources at rates of 1.0, 0.50, 0.25 , and 0.10 bits per source symbol. The average distortion results were generally within 1 dB of the distortion-rate bound but varied widely depending on the source and rate. The results were compared with those for transform quantization simulations for the same sources and rates. The tree code always performed better but only by an average of 0.44 dB all sources and rates. Longer source blocks and more intensive search would certainly improve the performance of the tree codes, but at the expense of extra computation and storage.

A comparative study of multiple attribute tree and inverted file structures for large bibliographic files

Abstract: A variety of data structures such as inverted file, multi-lists, quad tree, k-d tree, range tree, polygon tree, quintary tree, multidimensional tries, segment tree, doubly chained tree, the grid file, d-fold tree. super B-tree, Multiple Attribute Tree (MAT), etc. have been studied for multidimensional searching and related problems. Physical data base organization, which is an important application of multidimensional searching, is traditionally and mostly handled by employing inverted file. This study proposes MAT data structure for bibliographic file systems, by illustrating the superiority of MAT data structure over inverted file. Both the methods are compared in terms of preprocessing, storage and query costs. Worst-case complexity analysis of both the methods, for a partial match query, is carried out in two cases: (a) when directory resides in main memory, (b) when directory resides in secondary memory. In both cases, MAT data structure is shown to be more efficient than the inverted file method. Arguments are given to illustrate the superiority of MAT data structure in an average case also. An efficient adaptation of MAT data structure, that exploits the special features of MAT structure and bibliographic files, is proposed for bibliographic file systems. In this adaptation, suitable techniques for fixing and ranking of the attributes for MAT data structure are proposed. Conclusions and proposals for future research are presented.

The Sneptree - A Versatile Interconnection Network

Abstract: A new interconnection network, the Sneptree, is investigated. The Sneptree consists of 2 to the power of N–1 identical nodes and each node has four links. The links are connected to form an augmented complete binary tree where the outgoing links of the leaves are feedback to all the nodes in the network. We prove that a complete binary tree with arbitrary size can be mapped onto a Sneptree optimally. Hence, the Sneptree is particularly well suited for distributed computations with tree- structured computation graph, such as divide-and-conquer and backtracking. One type of Sneptree, which contains two disjoint spanning cycles and is thus called Cyclic Sneptree, is of particular interest since it can simulate a fully unbalanced tree optimally, such as a left/right skewed tree. A recursive method is given to generate the H-structure layout of the Cyclic Sneptree. The number of crossings and the length of the longest wires in the H-structure layout are analyzed. A message routing algorithm between any two leaf nodes is presented. The routing algorithm, which is of O(n) complexity, gives a good approximation to the shortest path. The traffic congestion in the nodes at the upper levels is also significantly reduced compared to the binary tree case.

Efficient algorithms to create and maintain balanced and threaded binary search trees

Abstract: The algorithm proposed by Chang and lyengar to perfectly balance binary search trees has been modified to not only balance but also thread binary search trees. Threads are constructed in the same sequence as normal pointers during the balancing process. No extra workspace is necessary, and the running time is also linear for the modified algorithm. Such produced tree structure has minimal average path length for fast information retrieval, and threads to facilitate more flexible and efficient traversing schemes. Maintenance and manipulation of the data structure are discussed and relevant algorithms given.

An n‐dimensional region data management system using combined tree structures

Abstract: In this paper we describe management system for region data using tree structures. Though the region data are divided into spatial data and alpha-numerical data, we are primarily concerned with the management of spatial data. In the proposed method the cellular data obtained by partitioning them into equally spaced meshes (the cells have regional IDs as values) are managed by using combined two-step binary tree structures. First, the three structures of the first step (primary structures) are constructed with the following procedure. (1) The object plane is recursively partitioned into two equal parts alternating vertically and horizontally, so that the number of kinds of regions contained in a small rectangle is two or less. (2) This partition procedure is represented by using a tree structure with two children (degree 2). Also, a secondary structure serves to distinguish the patterns of two regions in a rectangle given by a leaf of the primary structure and the representation by a simplified binary tree is used. The tree structures have the following characteristics. (1) Since global data on the whole object plane are obtained by the primary structure, range search can be conducted efficiently. (2) By using the simplified binary tree representation for the secondary structures, the total number of nodes is reduced to less than one half of that in an ordinary binary tree representation. (3) Since the operations for searching or overlaying are simplified, they can be executed at high speed.