Return to search

Polynomial kernelisation of H-free edge modification problems. / CUHK electronic theses & dissertations collection

關於有唯一禁子圖的改邊問題的多項式核心無H加/删/加删邊問題求是否可能加/删/加删至多k條邊於一圖使其無任何與H同構的誘導子圖。此乃計算機科學基本問題之一,其研究廣泛。此題對任意固定H為NP完全且固定參數可解。本文研究無H改邊問題之多項式核心;其存在視H之結構而定。之分類在當H為一圈,路徑或三聯通圖時則完全,當H為删一邊於完全圖之結果時則近完全,當H為樹時則部分此結果加強對無H改邊問題之認識。本文的思路與工具益未來研究,或有助於無H改邊問題多項式核心存在二分定理之發現。 / The H-free edge completion (deletion, editing) problem asks whether it is possible to add to (delete from, add to and delete from) a graph at most k edges so that no induced sub graph isomorphic to H remains. These problems are fundamental in computer science and were studied extensively. They are NP-complete and fixed-parameter tractable for every fixed H. / In this thesis, we study polynomial kernels for H-free edge modification problems, as their existence depends on the structure of H. We characterise their existence completely when H is a path, cycle or 3-connected graph, almost completely when H is one edge short of a complete graph, and partially when H is a tree. / These results enhance our understanding of H-free edge modification problems significantly. Our ideas and tools can be useful to future studies and may lead eventually to a dichotomy theorem on the existence of polynomial kernels for H-free edge modification problems. / Detailed summary in vernacular field only. / Cai, Yufei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 97-99). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Chapter 1 --- Preliminaries --- p.1 / Chapter 1.1 --- Edge modification problems and kernelisation --- p.2 / Chapter 1.2 --- Main results --- p.4 / Chapter 1.3 --- The lack of polynomial kernels --- p.5 / Chapter 1.4 --- Conventions and organisation --- p.8 / Chapter 2 --- Component Design --- p.11 / Chapter 2.1 --- Weighted satisficability on selective formulas --- p.12 / Chapter 2.2 --- 4-cycle --- p.15 / Chapter 2.3 --- The general scheme of component design --- p.20 / Chapter 2.4 --- Applications --- p.26 / Chapter 3 --- Local Alteration --- p.31 / Chapter 3.1 --- Bigger forbidden subgraphs from smaller ones --- p.32 / Chapter 3.2 --- Lifting the quarantine --- p.37 / Chapter 4 --- Circuit Implementation --- p.43 / Chapter 4.1 --- Monotone circuits --- p.44 / Chapter 4.2 --- Centralisation --- p.45 / Chapter 4.3 --- Implementation --- p.48 / Chapter 5 --- Kernel for Diamond-Free Edge Deletion --- p.55 / Chapter 5.1 --- Diamond-graphs --- p.56 / Chapter 5.2 --- The invariant things --- p.59 / Chapter 5.3 --- Correctness --- p.61 / Chapter 5.4 --- Lockets --- p.64 / Chapter 5.5 --- Representative systems of diamonds --- p.68 / Chapter 5.6 --- Kernel size --- p.70 / Chapter 6 --- Conclusions --- p.73 / Chapter 6.1 --- 3-connected forbidden subgraphs --- p.74 / Chapter 6.2 --- Cycles, paths and nearly complete graphs --- p.76 / Chapter 6.3 --- Trees --- p.77 / Chapter 6.4 --- Open problems --- p.79 / Chapter A --- List of Trees --- p.81 / Chapter B --- List of Problems --- p.83 / Chapter C --- Glossary --- p.87 / Chapter D --- Bibliography --- p.96

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328005
Date January 2012
ContributorsCai, Yufei., Chinese University of Hong Kong Graduate School. Division of Computer Science and Engineering.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatelectronic resource, electronic resource, remote, 1 online resource (iv, iv, 99 leaves) : ill.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Page generated in 0.0015 seconds