Showing papers on "Interval tree published in 1984"

Scaling and related techniques for geometry problems

Abstract: Three techniques in computational geometry are explored: Scaling solves a problem by viewing it at increasing levels of numerical precision; activation is a restricted type of update operation, useful in sweep algorithms; the Cartesian tree is a data structure for problems involving maximums and minimums. These techniques solve the minimum spanning tree problem in Rk1 and Rk

Analysis and Design of a Decision Tree Based on Entropy Reduction and Its Application to Large Character Set Recognition

Abstract: Based on a recursive process of reducing the entropy, the general decision tree classifier with overlap has been analyzed. Several theorems have been proposed and proved. When the number of pattern classes is very large, the theorems can reveal both the advantages of a tree classifier and the main difficulties in its implementation. Suppose H is Shannon's entropy measure of the given problem. The theoretical results indicate that the tree searching time can be minimized to the order O(H), but the error rate is also in the same order O(H) due to error accumulation. However, the memory requirement is in the order 0(H exp(H)) which poses serious problems in the implementation of a tree classifier for a large number of classes. To solve these problems, several theorems related to the bounds on the search time, error rate, memory requirement and overlap factor in the design of a decision tree have been proposed and some principles have been established to analyze the behaviors of the decision tree. When applied to classify sets of 64, 450, and 3200 Chinese characters, respectively, the experimental results support the theoretical predictions. For 3200 classes, a very high recognition rate of 99.88 percent was achieved at a high speed of 873 samples/s when the experiment was conducted on a Cyber 172 computer using a high-level language.

Efficient algorithms to globally balance a binary search tree

Abstract: A binary search tree can be globally balanced by readjustment of pointers or with a sorting process in O(n) time, n being the total number of nodes This paper presents three global balancing algorithms, one of which uses folding with the other two adopting parallel procedures These algorithms show improvement in time efficiency over some sequential algorithms [1, 2, 7] when applied to large binary search trees A comparison of various algorithms is presented

Computing on a free tree via complexity-preserving mappings

Abstract: It appears that in a number of cases computing over free trees is no more difficult than computing over linear lists. In the arithmetic model, we have established a strict equivalence between the interval query problem and its generalization on a tree structure. In the reference machine model, the concept of efficiency is traditionally captured by the class of retrieval problems which can be solved in O(nP0LY LOG(n)) space and O(POLYLOG(n)) time. We have shown that in a number of examples this class is closed under transformations from lists to trees. Characterizing the set of problems and techniques for which this holds is an interesting open problem.

A Comparative Study Of X-Tree, Pyramid And Related Machines

Abstract: The intent of this paper was to investigate data movement techniques for some special networks which are derived from the binary tree and the mesh machines. We presented optimal bounds for some problems and close bounds for others. A new lower bound technique which incorporates the entire network topdogy was introduced. We believe that this technique is quite powerful and can be exploited to yield good lower bounds for conservative flow algorithms on other networks. However, it seems to be diacult to generalize it for nonconservative flow algorithms. Though we have obtained close bounds, several problems that remain open are noted.

Solving Visibility Problems by Using Skeleton Structures

Abstract: This paper presents solutions to several visibility problems which can be considered as simplified versions of the hidden line elimination problem. We present a technique which allows to translate many line sweep algorithms involving sets of iso-oriented objects into algorithms for sets of non iso-oriented objects such that the asymptotic worst case time and space requirements do not change.

Index maintenance for non-uniform record distributions

Abstract: The file maintenance problem of organizing a collection of records is considered in this paper. Associated with each record is a key which uniquely identifies the record. The number of records to be stored is so large that the bulk of the records must reside on external storage even when transactions are in progress. The file organization must allow execution of operations insert. delete. update and range query. Both insert and delete allow the number of records within the file to change. And update provides for modifications t,o records alread! within the file. The range query operation returns all records in the file having keys k lvithin an interval ( 0, P ) , i.e. cr < k < ,fl into the user’s work space. The data structure scheme must process these operations on-line; that is. each operation must, run to completion before the next operation is input into the scheme. The literat,ure abounds with various organizational schemes for managing a collection of records to provide these operations. These schemes may be categorized into one of two types: 1) those that organize the specific set of records and 2) those that. organize the key space from -. which t.he records are drawn. A brief perspective of relevant data structures within this classification schemt is now presented. The first type is typified by comparative search strategies such as B-tree structured

An efficient VLSI dictionary machine

Abstract: A binary tree machine which can handle all the dictionary machine and priority queue operations as well as some other data queries is designed in this paper. This machine supports operations like Insert, Delete, Extract-Min/Max, Membership and Near and their redundant forms. If the number of keys present in the tree is n, then each of the operations takes O(log n) steps, and can be fed into the tree in a pipeline manner at a constant rate. A machine with N=2**s-1 processors can store upto N-s data elements. The output is generated at a fixed interval. It does not use any horizontal wires as in some previous designs. Moreover, this approach does not require any sorted-order, is potentially applicable to non-binary tree structures, and is significantly simpler to implement than all the previous designs.

The use of binary search trees in external distribution sorting

Abstract: A new method of external distribution sorting called tree partitioning is suggested. It involves the use of a binary tree to split an incoming file into successively smaller partitions until these are small enough to be sorted internally. The tree is generated from a sample of data of the same type as those to be sorted using that tree. The method is therefore suitable in cases where some regularity in the data is to be expected, as is the case, for example, with words from a textual or bibliographic database. The number of disc accesses during a tree partitioning sort were calculated in a simulation using files of up to 900,000 text words extracted from British National Bibliography catalogue files. These were compared with the actual numbers of disc accesses used by a standard sort-merge utility. Although the differences were in general not large, the comparison was favourable to tree partitioning in the majority of cases.

A Binary Tree Classifier for Ship Targets

Abstract: This paper describes the design of a binary tree classifier for ship targets The design methodology is general enough so that it can be utilized for other classification problems A hierarchical clustering procedure is employed to i) discover the underlying structure of data, and ii) construct the binary tree skeleton The best feature subset, at each nonterminal node of the tree skeleton, is selected through a multivariate stepwise procedure which attempts to maximize the class separability Further, this stepwise approach continues, until the probability of error at each nonterminal node with respect to a quadratic discriminant function is minimized The proposed tree classifier has been evaluated against 1300 samples and classification accuracy of 85% versus 62% for the single stage classifier is achieved

A unified algorithm for computer-aided fault tree analysis

Abstract: A unified algorithm for computer-aided fault tree analysis is presented in this paper. Byusing this algorithm, all the modular subtrees of the primal fault tree can be found, the dis-joint implicant families of each modular subtree and its dual can be obtained, the primeimplicant family of the primal fault tree can be given, and the conventional quantitativecomputation and some new quantitative analysis can also be done. It is more complete andefficient as compared with Willie's algorithm.

Generation and Termination of Binary Decision Trees for Nonparametric Multiclass Classification.

Abstract: : A two-step procedure for nonparametric multiclass classifier design is described. A multiclass recursive partioning algorithm is given which generated a single binary decision tree for classifying all classes. The algorithm minimizes the Bayes risk at each node. A tree termination algorithm is given which optimally terminates binary decision trees. The algorithm yields the unique tree with fewest nodes which minimizes the Bayes risk. Tree generation and termination are based on the training and test samples, respectively.