The Power of Linear Programming for Valued CSPs
A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the language with the goal to minimise the sum. This framework includ...
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| Format: | Conference item |
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2012
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| _version_ | 1826257556577714176 |
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| author | Thapper, J Zivny, S |
| author_facet | Thapper, J Zivny, S |
| author_sort | Thapper, J |
| collection | OXFORD |
| description | A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the language with the goal to minimise the sum. This framework includes and generalises well-studied constraint satisfaction problems (CSPs) and maximum constraint satisfaction problems (Max-CSPs). Our main result is a precise algebraic characterisation of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation. Using this result, we obtain tractability of several novel and previously widely-open classes of VCSPs, including problems over valued constraint languages that are: (1) submodular on arbitrary lattices; (2) bisubmodular (also known as k-submodular) on arbitrary finite domains; (3) weakly (and hence strongly) tree-submodular on arbitrary trees. |
| first_indexed | 2024-03-06T18:20:06Z |
| format | Conference item |
| id | oxford-uuid:05fd2ad2-c9c1-4d11-a878-14a6acab1f5a |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:20:06Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:05fd2ad2-c9c1-4d11-a878-14a6acab1f5a2022-03-26T09:00:09ZThe Power of Linear Programming for Valued CSPsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:05fd2ad2-c9c1-4d11-a878-14a6acab1f5aSymplectic Elements at Oxford2012Thapper, JZivny, SA class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the language with the goal to minimise the sum. This framework includes and generalises well-studied constraint satisfaction problems (CSPs) and maximum constraint satisfaction problems (Max-CSPs). Our main result is a precise algebraic characterisation of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation. Using this result, we obtain tractability of several novel and previously widely-open classes of VCSPs, including problems over valued constraint languages that are: (1) submodular on arbitrary lattices; (2) bisubmodular (also known as k-submodular) on arbitrary finite domains; (3) weakly (and hence strongly) tree-submodular on arbitrary trees. |
| spellingShingle | Thapper, J Zivny, S The Power of Linear Programming for Valued CSPs |
| title | The Power of Linear Programming for Valued CSPs |
| title_full | The Power of Linear Programming for Valued CSPs |
| title_fullStr | The Power of Linear Programming for Valued CSPs |
| title_full_unstemmed | The Power of Linear Programming for Valued CSPs |
| title_short | The Power of Linear Programming for Valued CSPs |
| title_sort | power of linear programming for valued csps |
| work_keys_str_mv | AT thapperj thepoweroflinearprogrammingforvaluedcsps AT zivnys thepoweroflinearprogrammingforvaluedcsps AT thapperj poweroflinearprogrammingforvaluedcsps AT zivnys poweroflinearprogrammingforvaluedcsps |