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Computational analysis of the random components induced by a binary equivalence relation


Balbine, Guy de (1968) Computational analysis of the random components induced by a binary equivalence relation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2A9K-P464.


The problem of partitioning into classes by means of a binary equivalence relation is investigated. Several algorithms for determining the number of components in the graph associated with a particular set of elements are constructed and compared. When the classification process operates on independently drawn samples of n distinct elements from a population, the expected number of components is shown to be obtainable recursively for a class of problems called separable; in all cases, estimates are available to reach any desired level of accuracy. Clustering models in Euclidean space are analyzed in detail and asymptotic formulas obtained to complement experiments. Conjectures concerning the general behavior of the expected number of components are presented also. Finally, several computational tools of general interest are improved significantly.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Engineering and Applied Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Franklin, Joel N.
Thesis Committee:
  • Franklin, Joel N. (chair)
  • Knuth, Donald E.
  • McCann, Gilbert Donald
  • Locke, Kenneth
Defense Date:17 April 1968
Non-Caltech Author Email:gdebalbine (AT)
Record Number:CaltechETD:etd-11102005-145557
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4495
Deposited By: Imported from ETD-db
Deposited On:10 Nov 2005
Last Modified:21 Dec 2019 03:59

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PDF (Balbine_g_1968.pdf) - Final Version
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