| Author: | Ke, Yuping |
| Title: | Kernelization for edge modification problems |
| Advisors: | Cao, Yixin (COMP) |
| Degree: | Ph.D. |
| Year: | 2023 |
| Subject: | Graph theory Graph algorithms Computer algorithms Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Computing |
| Pages: | x, 151 pages : color illustrations |
| Language: | English |
| Abstract: | Graph modification problems are significant problems in computer science that have gained considerable attention in recent decades. In this thesis, we focus on edge modification problems, whose task is to make an input graph satisfy some required properties by making small changes to the edges in the graph. We study kernelization algorithms for edge modification problems toward several graph classes that can be characterized by a finite set of forbidden induced subgraphs and provide small kernels for these problems. A kernelization algorithm is a preprocessing algorithm that reduces the input instances to an equivalent instance with a smaller size in polynomial time. We show that the edge deletion problem toward cluster graphs and the edge addition problem toward paw-free graphs admit linear kernels, a 2k-vertex kernel for the former one and a 38k-vertex kernel for the latter one. In addition, we prove that the edge addition problem toward trivially perfect graphs admits a quadratic kernel. We also prove that the edge addition problem and the edge deletion problem toward (pseudo-) split graphs have a kernel with O(K1.5) vertices. |
| Rights: | All rights reserved |
| Access: | open access |
Copyright Undertaking
As a bona fide Library user, I declare that:
- I will abide by the rules and legal ordinances governing copyright regarding the use of the Database.
- I will use the Database for the purpose of my research or private study only and not for circulation or further reproduction or any other purpose.
- I agree to indemnify and hold the University harmless from and against any loss, damage, cost, liability or expenses arising from copyright infringement or unauthorized usage.
By downloading any item(s) listed above, you acknowledge that you have read and understood the copyright undertaking as stated above, and agree to be bound by all of its terms.
Please use this identifier to cite or link to this item:
https://theses.lib.polyu.edu.hk/handle/200/12563