Maximizing determinants under partition constraints

  title={Maximizing determinants under partition constraints},
  author={Aleksandar Nikolov and Mohit Singh},
Given a positive semidefinte matrix L whose columns and rows are indexed by a set U, and a partition matroid M=(U, I), we study the problem of selecting a basis B of M such that the determinant of the submatrix of L induced by the rows and columns in B is maximized. This problem appears in many areas including determinantal point processes in machine learning, experimental design, geographical placement problems, discrepancy theory and computational geometry to model subset selection problems… CONTINUE READING
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