A linear space algorithm for computing maximal common subsequences
Communications of the ACM
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We study an alignment called a packing alignment that is an alignment for sequences of various length events like musical notes. One event in a packing alignment can have a number of consecutive opposing events unless the total length of them exceeds the length of that one event. Instead of using a score function that depends on event length, which was studied by Mongeau and Sankoff [5], packing alignment deals with event lengths explicitly using a simple score function. This makes the problem clearer as an optimization problem. Packing alignment can be calculated efficiently using dynamic programming. As an application of packing alignment, we conducted experiments on frequent approximate pattern extraction from MIDI files of famous musical variations. The patterns and occurrences extracted from the variations using packing alignment have more appropriate boundaries than those using conventional string alignments from the viewpoints of the repetition structure of the variations.