UMI  
ProQuest® Dissertations & Theses
The world's most comprehensive collection of dissertations and theses. Learn more...
ProQuest  
 
 
Design and analysis of data structures for dynamic trees
by Werneck, Renato F., PhD, PRINCETON UNIVERSITY, 2006, 0 pages; 3214596
 

Abstract: The dynamic trees problem is that of maintaining a forest that changes over time through edge insertions and deletions. We can associate data with vertices or edges and manipulate this data, individually or in bulk, with operations that deal with whole paths or trees. Efficient solutions to this problem have numerous applications, particularly in algorithms for network flows and dynamic graphs in general. Several data structures capable of logarithmic-time dynamic tree operations have been proposed. The first was Sleator and Tarjan's ST-tree, which represents a partition of the tree into paths. Although reasonably fast in practice, adapting ST-trees to different applications is nontrivial. Frederickson's topology trees, Alstrup et al.'s top trees, and Acar et al.'s RC-trees are based on tree contractions: they progressively combine vertices or edges to obtain a hierarchical representation of the tree. This approach is more flexible in theory, but all known implementations assume the trees have bounded degree; arbitrary trees are supported only after ternarization. This thesis shows how these two approaches can be combined (with very little overhead) to produce a data structure that is at least as generic as any other, very easy to adapt, and as practical as ST-trees. It can be seen as a self-adjusting implementation of top trees and provides a logarithmic bound per operation in the amortized sense. We also discuss a pure contraction-based implementation of top trees, which is more involved but guarantees a logarithmic bound in the worst case. Finally, an experimental evaluation of these two data structures, including a comparison with previous methods, is presented.

 
Advisor: Tarjan, Robert E.
School: PRINCETON UNIVERSITY
Source: DAI-B 67/04, p. 2091, Oct 2006
Source Type: PhD
Subjects: Computer science
Publication Number: 3214596
     
Adobe PDF Access the complete dissertation:
 

» Find an electronic copy at your library.
  Use the link below to access a full citation record of this graduate work:
  http://gateway.proquest.com/openurl%3furl_ver=Z39.88-2004%26res_dat=xri:pqdiss%26rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation%26rft_dat=xri:pqdiss:3214596
  If your library subscribes to the ProQuest Dissertations & Theses (PQDT) database, you may be entitled to a free electronic version of this graduate work. If not, you will have the option to purchase one, and access a 24 page preview for free (if available).

 
 
 

About ProQuest Dissertations & Theses
With over 2.3 million records, the ProQuest Dissertations & Theses (PQDT) database is the most comprehensive collection of dissertations and theses in the world. It is the database of record for graduate research.

The database includes citations of graduate works ranging from the first U.S. dissertation, accepted in 1861, to those accepted as recently as last semester. Of the 2.3 million graduate works included in the database, ProQuest offers more than 1.9 million in full text formats. Of those, over 860,000 are available in PDF format. More than 60,000 dissertations and theses are added to the database each year.

If you have questions, please feel free to visit the ProQuest Web site - http://www.il.proquest.com - or call ProQuest Hotline Customer Support at 1-800-521-3042.



Copyright © 2007 ProQuest. All rights reserved. Terms and Conditions

ProQuest