Title page for ETD etd-05042006-164527
|Type of Document
||Juvvadi, Ramana Rao
||Perfect hashing and related problems
|Heath, Lenwood S.
|Allison, Donald C. S.
|Fox, Edward Alan
|Shaffer, Clifford A.
|Sherali, Hanif D.
- Hashing (Computer science)
|Date of Defense
One of the most common tasks in many computer applications is the maintenance of a
dictionary of words. The three most basic operations on the dictionary are find, insert, and
delete. An important data structure that supports these operations is a hash table. On a
hash table, a basic operation takes 0 (1) time in the average case and O( n) time in the worst
case, where n is the number of words in the dictionary. While an ordinary hash function
maps the words in a dictionary to a hash table with collisions, a perfect hash function maps
the words in a dictionary to a hash table with no collisions. Thus, perfect hashing is a
special case of hashing, in which a find operation takes 0(1) time in the worst case, and an
insert or a delete operation takes 0(1) time in the average case and O(n) time in the worst
This thesis addresses the following issues:
• Mapping, ordering and searching (MOS) is a successful algorithmic approach to finding
perfect hash functions for static dictionaries. Previously, no analysis has been given
for the running time of the MOS algorithm. In this thesis, a lower bound is proved on
the tradeoff between the time required to find a perfect hash function and the space
required to represent the perfect hash function .
• A new algorithm for static dictionaries called the musical chairs(MC) algorithm is
developed that is based on ordering the hyperedges of a graph. It is found experimentally
that the MC algorithm runs faster than the MOS algorithm in all cases for
which the MC algorithm is capable of finding a perfect hash function.
• A new perfect hashing algorithm is developed for dynamic dictionaries. In this algorithm,
an insert or a delete operation takes 0(1) time in the average case, and a find
operation takes 0(1) time in the worst case. The algorithm is modeled using results
from queueing theory .
• An ordering problem from graph theory, motivated by the hypergraph ordering problem
in the Me algorithm, is proved to be NP-complete.
|| Approximate Download Time
| 28.8 Modem
|| 56K Modem
|| ISDN (64 Kb)
|| ISDN (128 Kb)
|| Higher-speed Access
next to an author's name indicates that all
files or directories associated with their ETD
are accessible from the Virginia Tech campus network only.
If you have questions or technical
problems, please Contact DLA.