Sweepline the music!

Authors:
Esko Ukkonen;Kjell Lemström;Veli Mäkinen
Affiliations:
Department of Computer Science, University of Helsinki, P.O. Box 26 (Teollisuuskatu 23), FIN-00014 Helsinki, Finland;Department of Computer Science, University of Helsinki, P.O. Box 26 (Teollisuuskatu 23), FIN-00014 Helsinki, Finland;Department of Computer Science, University of Helsinki, P.O. Box 26 (Teollisuuskatu 23), FIN-00014 Helsinki, Finland
Venue:
Computer Science in Perspective
Year:
2003

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Abstract

The problem of matching sets of points or sets of horizontal line segments in plane under translations is considered. For finding the exact occurrences of a point set of size m within another point set of size n we give an algorithm with running time O(mn), and for finding partial occurrences an algorithm with running time O(mnlogm). To find the largest overlap between two line segment patterns we develop an algorithm with running time O(mnlog(mn)). All algorithms are based on a simple sweepline traversal of one of the patterns in the lexicographic order. The motivation for the problems studied comes from music retrieval and analysis.