Multiple alignment, communication cost, and graph matching
SIAM Journal on Applied Mathematics
Approximation algorithms for multiple sequence alignment
Theoretical Computer Science
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Pattern matching algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
ACM Computing Surveys (CSUR)
Computation of Normalized Edit Distance and Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
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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 editoperation 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.