Self-normalised distance with don't cares
We present O(n log m) algorithms for a new class of problems termed self-normalised distance with don't cares. The input is a pattern p of length m and text t of length n > m. The elements of these strings are either integers or wild card symbols. In the shift version, the problem is to...
| Main Authors: | , |
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| Format: | Conference item |
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2007
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| _version_ | 1826279187024969728 |
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| author | Clifford, P Clifford, R |
| author_facet | Clifford, P Clifford, R |
| author_sort | Clifford, P |
| collection | OXFORD |
| description | We present O(n log m) algorithms for a new class of problems termed self-normalised distance with don't cares. The input is a pattern p of length m and text t of length n > m. The elements of these strings are either integers or wild card symbols. In the shift version, the problem is to compute min α ∑j=0m-1 (α - pj - ti+j)2 for all i, where wild cards do not contribute to the sum. In the shift-scale version, the objective is to compute min αβ ∑j=0m-1 (α + βpj - ti+j)2 for all i, similarly. We show that the algorithms have the additional benefit of providing simple O(n log m) solutions for the problems of exact matching with don't cares, exact shift matching with don't cares and exact shift-scale matching with don't cares. © Springer-Verlag Berlin Heidelberg 2007. |
| first_indexed | 2024-03-06T23:55:01Z |
| format | Conference item |
| id | oxford-uuid:73e7c3e2-c4f7-4573-b7b2-dc952eebacab |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:55:01Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:73e7c3e2-c4f7-4573-b7b2-dc952eebacab2022-03-26T19:59:32ZSelf-normalised distance with don't caresConference itemhttp://purl.org/coar/resource_type/c_5794uuid:73e7c3e2-c4f7-4573-b7b2-dc952eebacabSymplectic Elements at Oxford2007Clifford, PClifford, RWe present O(n log m) algorithms for a new class of problems termed self-normalised distance with don't cares. The input is a pattern p of length m and text t of length n > m. The elements of these strings are either integers or wild card symbols. In the shift version, the problem is to compute min α ∑j=0m-1 (α - pj - ti+j)2 for all i, where wild cards do not contribute to the sum. In the shift-scale version, the objective is to compute min αβ ∑j=0m-1 (α + βpj - ti+j)2 for all i, similarly. We show that the algorithms have the additional benefit of providing simple O(n log m) solutions for the problems of exact matching with don't cares, exact shift matching with don't cares and exact shift-scale matching with don't cares. © Springer-Verlag Berlin Heidelberg 2007. |
| spellingShingle | Clifford, P Clifford, R Self-normalised distance with don't cares |
| title | Self-normalised distance with don't cares |
| title_full | Self-normalised distance with don't cares |
| title_fullStr | Self-normalised distance with don't cares |
| title_full_unstemmed | Self-normalised distance with don't cares |
| title_short | Self-normalised distance with don't cares |
| title_sort | self normalised distance with don t cares |
| work_keys_str_mv | AT cliffordp selfnormaliseddistancewithdontcares AT cliffordr selfnormaliseddistancewithdontcares |