Abstract
A break in a {0, 1}-matrix is defined as a 0 with at least one 1 to its left and at least one 1 to its right in the same row. This paper is concerned with {0, 1}-matrices with given column sums and an upper limit for the row sums. In addition, there are limits on the distance from the first to the last 1 in a row. The problem that is considered is to find a {0, 1}-matrix satisfying the conditions such that the total number of breaks is minimum. An algorithm for solving this problem is presented. Computational results illustrate the effectiveness of the algorithm.
The investigation originated in a problem of crew rostering.
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Salzborn, F.J.M. Break minimization. Mathematical Programming 8, 43–53 (1975). https://doi.org/10.1007/BF01580427
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DOI: https://doi.org/10.1007/BF01580427