Exact Cover Problem in Milton Babbitt’s All-Partition Array
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One aspect of analyzing Milton Babbitt’s (1916–2011) all-partition arrays requires finding a sequence of distinct, non-overlapping aggregate regions that completely and exactly covers an irregular matrix of pitch class integers. This is an example of the so-called exact cover problem. Given a set, A, and a collection of distinct subsets of this set, S, then a subset of S is an exact cover of A if it exhaustively and exclusively partitions A. We provide a backtracking algorithm for solving this problem in an all-partition array and compare the output of this algorithm with an analysis produced manually.
KeywordsBabbitt Knuth All-partition array Exact cover Computational music analysis
The work reported in this paper was carried out as part of the EC-funded collaborative project, “Learning to Create” (Lrn2Cre8). The Lrn2Cre8 project acknowledges the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, under FET grant number 610859.
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