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Expected length of longest common subsequences
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Dancík, Vladimír (1994) Expected length of longest common subsequences. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3216371~S15
Abstract
A longest common subsequence of two sequences is a sequence that is a subsequence of both the given sequences and has largest possible length. It is known that the expected length of a longest common subsequence is proportional to the length of the given sequences. The proportion, denoted by 7k, is dependent on the alphabet size k and the exact value of this proportion is not known even for a binary alphabet.
To obtain lower bounds for the constants 7k, finite state machines computing a common subsequence of the inputs are built. Analysing the behaviour of the machines for random inputs we get lower bounds for the constants 7k. The analysis of the machines is based on the theory of Markov chains. An algorithm for automated production of lower bounds is described.
To obtain upper bounds for the constants 7k, collations pairs of sequences with a marked common subsequence - are defined. Upper bounds for the number of collations of ‘small size’ can be easily transformed to upper bounds for the constants 7k. Combinatorial analysis is used to bound the number of collations. The methods used for producing bounds on the expected length of a common subsequence of two sequences are also used for other problems, namely a longest common subsequence of several sequences, a shortest common supersequence and a maximal adaptability.
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||
| Library of Congress Subject Headings (LCSH): | Sequential machine theory, Sequences (Mathematics), Markov processes -- industrial applications, Combinatorial analysis -- industrial applications | ||||
| Official Date: | 1994 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Department of Computer Science | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Paterson, Michael S. | ||||
| Sponsors: | University of Warwick ; Council of Vice Chancellors and Principals ; European Research Council | ||||
| Extent: | viii, 135 leaves : charts | ||||
| Language: | eng |
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