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Some new results on constructing optimal alphabetic binary trees Mumey, Brendan M.
Abstract
This thesis studies the question of whether optimal alphabetic binary trees can be constructed in o(n lg n) time. Hu and Tucker [1] gave the first subquadratic algorithm in 1971, namely an O(n lg n) time algorithm. Optimal alphabetic binary trees have many applications and the question of whether an o(n lg n) time algorithm exists has remained an open problem in data structures for the last 20 years. We show that a class of techniques for finding optimal alphabetic trees which includes all current methods yielding O(n lg n) time algorithms are at least as hard as sorting in whatever model of computation used. We introduce a new idea for finding optimal alphabetic binary trees which we refer to as region-processing. Region-processing methods have been successfully used to give O(n) time algorithms for the case where all the input weights are within a constant factor of one another and when they are exponentially separated. Although the region based method we give exhibits o(n lg n) time performance for many cases, we also show a reduction from sorting to it as well. It is possible that the ideas used in this reduction can be extended to yield a general ω(n) lower bound.
Item Metadata
Title |
Some new results on constructing optimal alphabetic binary trees
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1992
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Description |
This thesis studies the question of whether optimal alphabetic binary trees can be constructed in o(n lg n) time. Hu and Tucker [1] gave the first subquadratic algorithm in
1971, namely an O(n lg n) time algorithm. Optimal alphabetic binary trees have many
applications and the question of whether an o(n lg n) time algorithm exists has remained
an open problem in data structures for the last 20 years. We show that a class of techniques for finding optimal alphabetic trees which includes all current methods yielding
O(n lg n) time algorithms are at least as hard as sorting in whatever model of computation used. We introduce a new idea for finding optimal alphabetic binary trees which we
refer to as region-processing. Region-processing methods have been successfully used to
give O(n) time algorithms for the case where all the input weights are within a constant
factor of one another and when they are exponentially separated. Although the region
based method we give exhibits o(n lg n) time performance for many cases, we also show
a reduction from sorting to it as well. It is possible that the ideas used in this reduction
can be extended to yield a general ω(n) lower bound.
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Extent |
811368 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-01-06
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0051343
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1992-05
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.