Abstract
Scoring matrices are widely used in sequence comparisons. A scoring matrix γ is indexed by symbols of an alphabet. The entry in γ in row a and column b measures the cost of the edit operation of replacing symbol a by symbol b.
For a given scoring matrix and sequences s and t, we consider two kinds of induced scoring functions. The first function, known as weighted edit distance, is defined as the sum of costs of the edit operations required to transform s into t. The second, known as normalized edit distance, is defined as the minimum quotient between the sum of costs of edit operations to transform s into t and the number of the corresponding edit operations.
In this work we characterize the class of scoring matrices for which the induced weighted edit distance is actually a metric. We do the same for the normalized edit distance.
This research was partially supported by FAPESP/CNPq (PRONEX 2003/09925-5) and CNPq (Universal 478329/2004-0).
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© 2006 Springer-Verlag Berlin Heidelberg
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Araújo, E., Soares, J. (2006). Scoring Matrices That Induce Metrics on Sequences. In: Correa, J.R., Hevia, A., Kiwi, M. (eds) LATIN 2006: Theoretical Informatics. LATIN 2006. Lecture Notes in Computer Science, vol 3887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11682462_11
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DOI: https://doi.org/10.1007/11682462_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32755-4
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