All maximal-pairs in step-leap representation of melodic sequence

This paper proposes an efficient pattern extraction algorithm that can be applied on melodic sequences that are represented as strings of abstract intervallic symbols; the melodic representation introduces special ''binary don't care'' symbols for intervals that may belong to two partially overlapping intervallic categories. As a special case the well established ''step-leap'' representation is examined. In the step-leap representation, each melodic diatonic interval is classified as a step (+/-s), a leap (+/-l) or a unison (u). Binary don't care symbols are used to represent the possible overlapping between the various abstract categories e.g. *=s, *=l and #=-s, #=-l. We propose an O(n+d(n-d)+z)-time algorithm for computing all maximal-pairs in a given sequence x=x[1..n], where x contains d occurrences of binary don't cares and z is the number of reported maximal-pairs.

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