Bemman B., Meredith D. (2015) Exact Cover Problem in Milton Babbitt’s All-Partition Array. In: Collins T., Meredith D., Volk A. (eds) Mathematics and Computation in Music. MCM 2015. Lecture Notes in Computer Science, vol 9110. Springer, Cham
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.
Babbitt Knuth All-partition array Exact cover Computational music analysis