Transforming static data structures to dynamic structures

@article{Saxe1979TransformingSD,
  title={Transforming static data structures to dynamic structures},
  author={James B. Saxe and Jon Louis Bentley},
  journal={20th Annual Symposium on Foundations of Computer Science (sfcs 1979)},
  year={1979},
  pages={148-168}
}
  • J. SaxeJ. Bentley
  • Published 29 October 1979
  • Computer Science
  • 20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
In this paper we will investigate transformations that serve as tools in the design of new data structures. Specifically, we study general methods for converting static structures (in which all elements are known before any searches are performed) to dynamic structures (in which the insertion of a new element can be mixed with searches). We will see three classes of such transformations (each based on a different counting scheme for representing the integers) and then use a combinatorial model… 
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References

SHOWING 1-10 OF 30 REFERENCES

An Alphard Specification of a Correct and Efficient Transformation on Data Structures

This paper discusses one of Bentley and Saxe's transformations for converting solutions of simple searching problems to solutions of more complex problems, and specifies precisely the transformation and its conditions of applicability, and proves its correctness.

A transformation for adding range restriction capability to dynamic data structures for decomposable

A transformation is presented which enables range restrictions to be added to an arbitrary dynamic data structure on n elements, provided that the problem satisfies a certain decomposability condition, and that the authors are willing to allow increases of a factor of log n in the worst-case time for an operation and in the space used.

Efficient worst-case data structures for range searching

This paper investigates the worst-case complexity of range searching: preprocess N points in k-space such that range queries can be answered quickly, and develops three different structures for range searching that have absolutely optimal query time, but have very high preprocessing and storage costs.

Predicate-Oriented Database Search Algorithms

  • D. Willard
  • Computer Science
    Outstanding Dissertations in the Computer Sciences
  • 1978
This thesis will lay the foundations of the theory that should be used in the development of automatic predicate searching algorithms and show that the health of the computer industry requires lower software development costs.

A data structure for orthogonal range queries

  • G. S. Lueker
  • Computer Science
    19th Annual Symposium on Foundations of Computer Science (sfcs 1978)
  • 1978
It is shown that a decision tree of height O(dn log n) can be constructed to process n operations in d dimensions, suggesting that the standard decision tree model will not provide a useful method for investigating the complexity of orthogonal range queries.

A data structure for manipulating priority queues

A data structure is described which can be used for representing a collection of priority queues. The primitive operations are insertion, deletion, union, update, and search for an item of earliest…

Partial-Match Retrieval Algorithms

A new class of combinatorial designs (called associative block designs) provides better hash functions with a greatly reduced worst-case number of lists examined, yet with optimal average behavior maintained.

A New Approach to Planar Point Location

This paper presents a practical algorithm which runs in less than $6\lceil {\log _2 n} \rceil $ comparisons on a data structure which uses O(n\log n) storage, in the worst case.

A Problem in Multivariate Statistics: Algorithm, Data Structure and Applications.

A multidimensional divide-and-conquer technique is employed that gives rise to a compact data structure for geometric and statistical search problems and a large number of important statistical quantities are computed much faster than was previously possible.

Application of a Planar Separator Theorem

Any n-vertex planar graph has the property that it can be divided into components of roughly equal size by removing only O(√n) vertices. This separator theorem, in combination with a…