New upper bounds on the decomposability of planar graphs and fixed parameter algorithms
It is known that a planar graph on n vertices has branch-width/tree-width bounded by alphasqrt{n}. In many algorithmic applications it is useful to have a small bound on the constant alpha. We give a proof of the best, so far, upper bound for the constant alpha. In particular, for the case of tree-w...
| Authors: | ; |
|---|---|
| Format: | Report |
| Publication date: | 2002 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/97430 |
| Online Access: | https://hdl.handle.net/2117/97430 |
| Access Level: | Open access |
| Keyword: | Planar graphs Decomposability Fixed parameter algorithms Tree-width Branch-width Separation theorems Vertex cover Dominating set Àrees temàtiques de la UPC::Informàtica |
| _version_ | 1878733528069308416 |
|---|---|
| author | Fomin, Fedor V. |
| author2 | Thilikos Touloupas, Dimitrios |
| author2_role | author |
| author_browse | Fomin, Fedor V. Thilikos Touloupas, Dimitrios |
| author_facet | Fomin, Fedor V. Thilikos Touloupas, Dimitrios |
| author_role | author |
| collection | UPCommons. Portal del coneixement obert de la UPC |
| description | It is known that a planar graph on n vertices has branch-width/tree-width bounded by alphasqrt{n}. In many algorithmic applications it is useful to have a small bound on the constant alpha. We give a proof of the best, so far, upper bound for the constant alpha. In particular, for the case of tree-width, alpha<3.182 and for the case of branch-width, alpha<2.122. Our proof is based on the planar separation theorem of Alon, Seymour & Thomas and some min-max theorem of the graph minors series. Based on these bounds we introduce a new method for solving different fixed parameter problems on planar graphs. We prove that our method provides the best so far exponential speed-up for fundamental problems on planar graphs like Vertex Cover, Dominating Set, Independent Set and many others. |
| eu_rights_str_mv | openAccess |
| format | report |
| id | ES_57ef8fb27bd1dfd67286b2a0d2eb3abf |
| institution | Universitat Politècnica de Catalunya (UPC) |
| instname_str | Universitat Politècnica de Catalunya (UPC) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:upcommons.upc.edu:2117/97430 |
| publishDate | 2002 |
| publishDateSort | 2002 |
| reponame_str | UPCommons. Portal del coneixement obert de la UPC |
| spelling | New upper bounds on the decomposability of planar graphs and fixed parameter algorithms Fomin, Fedor V. Thilikos Touloupas, Dimitrios Planar graphs Decomposability Fixed parameter algorithms Tree-width Branch-width Separation theorems Vertex cover Dominating set Àrees temàtiques de la UPC::Informàtica It is known that a planar graph on n vertices has branch-width/tree-width bounded by alphasqrt{n}. In many algorithmic applications it is useful to have a small bound on the constant alpha. We give a proof of the best, so far, upper bound for the constant alpha. In particular, for the case of tree-width, alpha<3.182 and for the case of branch-width, alpha<2.122. Our proof is based on the planar separation theorem of Alon, Seymour & Thomas and some min-max theorem of the graph minors series. Based on these bounds we introduce a new method for solving different fixed parameter problems on planar graphs. We prove that our method provides the best so far exponential speed-up for fundamental problems on planar graphs like Vertex Cover, Dominating Set, Independent Set and many others. https://hdl.handle.net/2117/97430 |
| spellingShingle | New upper bounds on the decomposability of planar graphs and fixed parameter algorithms Fomin, Fedor V. Planar graphs Decomposability Fixed parameter algorithms Tree-width Branch-width Separation theorems Vertex cover Dominating set Àrees temàtiques de la UPC::Informàtica |
| title | New upper bounds on the decomposability of planar graphs and fixed parameter algorithms |
| title_full | New upper bounds on the decomposability of planar graphs and fixed parameter algorithms |
| title_fullStr | New upper bounds on the decomposability of planar graphs and fixed parameter algorithms |
| title_full_unstemmed | New upper bounds on the decomposability of planar graphs and fixed parameter algorithms |
| title_short | New upper bounds on the decomposability of planar graphs and fixed parameter algorithms |
| title_sort | New upper bounds on the decomposability of planar graphs and fixed parameter algorithms |
| topic | Planar graphs Decomposability Fixed parameter algorithms Tree-width Branch-width Separation theorems Vertex cover Dominating set Àrees temàtiques de la UPC::Informàtica |
| topic_facet | Planar graphs Decomposability Fixed parameter algorithms Tree-width Branch-width Separation theorems Vertex cover Dominating set Àrees temàtiques de la UPC::Informàtica |
| url | https://hdl.handle.net/2117/97430 |