Results in Computational Geometry: Geometric Embeddings and Query- Retrieval Problems

Abstract

Many fundamental questions in computational geometry arise from the consideration of distributions of points in euclidean space. This thesis explores two important ares of computational geometry in this setting: geometric embeddings and query-retrieval problems. Each area is addressed in a separate part of the thesis. Part I examines the geometric embedding problem for many of the graphs which are important in the study of parallel computation. Part II of this thesis examines query-retrieval problems concerning distributions of points in euclidean space. In this part, we describe a new technique for solving a variety of query-retrieval problems in optimal time with optimal or near optimal space. Our compaction technique incorporates planar separators, filtering search, and the probabilistic method for discrepancy problems.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1990
Accession Number
ADA230380

Entities

People

  • Mark D. Hansen

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Aspect Ratio
  • Computations
  • Computer Science
  • Computers
  • Computing System Architectures
  • Differential Equations
  • Embedding
  • Geometry
  • Mathematics
  • Parallel Computing
  • Parallel Processing
  • Parallel Processors
  • Probability
  • Three Dimensional
  • Two Dimensional

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space