In quest of an improved algorithm for transforming plane triangulations by simultaneous flips
This thesis is submitted in partial fulfillment of the requirements for the degree of Bachelor of Science in Computer Science, 2022.
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Brac University
2023
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| Rochtain ar líne: | http://hdl.handle.net/10361/18198 |
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10361-181982023-04-30T21:02:06Z In quest of an improved algorithm for transforming plane triangulations by simultaneous flips Prapty, Annesha Chowdhury Pranty, Namira Mustafiz Ahmed, Tasnova Mehnaz, Tasnuba Kaykobad, Mohammad Kaykobad, M Tanvir Department of Computer Science and Engineering, Brac University Algorithm Plane triangulations Simultaneous flips Computer algorithms This thesis is submitted in partial fulfillment of the requirements for the degree of Bachelor of Science in Computer Science, 2022. Cataloged from PDF version of thesis. Includes bibliographical references (pages 44-45). In this thesis we have studied the problem of transforming one plane triangulation into another by simultaneous flips of diagonals. A triangulation is a simple planar graph consisting of only 3-cycle (triangles) faces including outerface. In a triangulation, every edge lies on two faces that form a quadrilateral. An edge flipping is an operation that replaces this edge which is a diagonal of its corresponding quadrilateral with the other diagonal of the quadrilateral. A simultaneous flip set is an edge set of a triangulation that when flipped, the resulting graph is still a triangulation. Initially, it was proved that any two triangulations of equal order (number of vertices of a graph) can be transformed from one to another using a finite sequence of edge flip operations. Later on, it was observed that to complete this transformation, O(n log n) individual flips are enough. In the continuation of the research, an algorithm was established which states that the transformation can be done in 327.1 log(n) simultaneous flips. Lately, two algorithms were introduced to improve the leading coefficient of this bound for transforming any plane triangulation into another. These two algorithms lower this bound down to 85.8 log(n) and 45.6 log(n) respectively. In this thesis, we have developed an algorithm to introduce two dominant vertices simultaneously. Using our algorithm, any pair of vertices of the triangulation can be made dominant. The process requires at most 60.8 log(n) simultaneous flips. Annesha Chowdhury Prapty Namira Mustafiz Pranty Tasnova Ahmed Tasnuba Mehnaz B. Computer Science 2023-04-30T08:07:46Z 2023-04-30T08:07:46Z 2022 2022-05 Thesis ID 19101453 ID 19101449 ID 19101462 ID 19101627 http://hdl.handle.net/10361/18198 en Brac University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. 45 pages application/pdf Brac University |
| institution |
Brac University |
| collection |
Institutional Repository |
| language |
English |
| topic |
Algorithm Plane triangulations Simultaneous flips Computer algorithms |
| spellingShingle |
Algorithm Plane triangulations Simultaneous flips Computer algorithms Prapty, Annesha Chowdhury Pranty, Namira Mustafiz Ahmed, Tasnova Mehnaz, Tasnuba In quest of an improved algorithm for transforming plane triangulations by simultaneous flips |
| description |
This thesis is submitted in partial fulfillment of the requirements for the degree of Bachelor of Science in Computer Science, 2022. |
| author2 |
Kaykobad, Mohammad |
| author_facet |
Kaykobad, Mohammad Prapty, Annesha Chowdhury Pranty, Namira Mustafiz Ahmed, Tasnova Mehnaz, Tasnuba |
| format |
Thesis |
| author |
Prapty, Annesha Chowdhury Pranty, Namira Mustafiz Ahmed, Tasnova Mehnaz, Tasnuba |
| author_sort |
Prapty, Annesha Chowdhury |
| title |
In quest of an improved algorithm for transforming plane triangulations by simultaneous flips |
| title_short |
In quest of an improved algorithm for transforming plane triangulations by simultaneous flips |
| title_full |
In quest of an improved algorithm for transforming plane triangulations by simultaneous flips |
| title_fullStr |
In quest of an improved algorithm for transforming plane triangulations by simultaneous flips |
| title_full_unstemmed |
In quest of an improved algorithm for transforming plane triangulations by simultaneous flips |
| title_sort |
in quest of an improved algorithm for transforming plane triangulations by simultaneous flips |
| publisher |
Brac University |
| publishDate |
2023 |
| url |
http://hdl.handle.net/10361/18198 |
| work_keys_str_mv |
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