Finite state properties of bounded parthwidth graphs
| dc.contributor.author | Lu, Xiuyan | en_US |
| dc.date.accessioned | 2024-08-14T21:07:32Z | |
| dc.date.available | 2024-08-14T21:07:32Z | |
| dc.date.copyright | 1993 | en_US |
| dc.date.issued | 1993 | |
| dc.degree.department | Department of Computer Science | |
| dc.degree.level | Master of Science M.Sc. | en |
| dc.description.abstract | The concepts of the treewidth and pathwidth of combinatorial structures have come to play a central role in a number of important developments in discrete mathematics and combinatorial algorithm design. In particular, they are of fundamental importance to several general algorithm design techniques that provide an interesting line of attack for many problems that are NP-complete. This approach to algorithm design involves two basic steps: (1) the representation of the combinatorial structure by a string or tree of symbols over a finite alphabet (termed a parse of the structure), and (2) finite-state recognition of these representations. The project reported on here explores several issues regarding this approach to algorithm design that must be adequately resolved in order for these general theoretical developments to deliver useful algorithms. In particular, these issues concern several junctures where large hidden constants may hinder this approach. Since most of the tools of theory are relatively insensitive to constants, the project has centered on an experimental methodology, and on developing general software to support the exploration of these issues. In this setting, the experiments necessarily involve some preliminary theoretical work. There are three main results of this project. First, we identify a set of structural operators that are sufficient to parse graphs of bounded pathwidth, and prove this sufficiency. Secondly, based on this parsing scheme we have implemented a general software system for studying finite-state recognition of families of graphs of bounded path width represented as structural parses. Finally, we have used this software to explore the finite-state recognition of Hamiltonian graphs, obtaining data on the size of the resulting finite-state automata for the pathwidth bounds 2 and 3. | en |
| dc.format.extent | 60 pages | |
| dc.identifier.uri | https://hdl.handle.net/1828/18738 | |
| dc.rights | Available to the World Wide Web | en_US |
| dc.subject | UN SDG 9: Industry, Innovation, and Infrastructure | en |
| dc.title | Finite state properties of bounded parthwidth graphs | en_US |
| dc.type | Thesis | en_US |
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