Many geometry problems can be solved by transformation to graph problems. Often, both the geometry version and graph version of the problem are NP-hard - and therefore not likely to be solved in polynomial time. One approach to solving these hard problems is to use fixed parameter tractable (FPT) algorithms. We present a framework for developing FPT algorithms for graph problems using dynamic programming, monadic second order logic of graphs, tree-width, and bidimensionality. We use this framework to obtain FPT results for covering tour problems on grid-graphs with turn costs. The results for these problems are not practical, but they demonstrate how the basic framework can be used to quickly obtain FPT results. We provide suggestions on further research to improve our FPT results and to apply our framework to obtain new FPT results.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.111595 |
| Date | January 2008 |
| Creators | Yu, Nuo, 1983- |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (School of Computer Science.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 003163601, proquestno: AAIMR66898, Theses scanned by UMI/ProQuest. |
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