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All maximal-pairs in step-leap representation of melodic sequence
Cambouropoulos, Emilios and Crochemore, Maxime and Iliopoulos, Costas S. and Mohamed, Manal and Sagot, Marie-France (2007) All maximal-pairs in step-leap representation of melodic sequence. Information Sciences, 177 (9). pp. 1954-1962.
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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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