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This paper describes an NP-hard combinatorial optimization problem arising in the Sloan Digital Sky Survey and a practical approximation algorithm that has been implemented and will be used in the survey. The algorithm is based on network flow theory and Lagrangian relaxation.
The Hall polynomialg λμν (p) counts subgroups of type ν and cotype μ in a finite abelianp-group of type λ. We derive a formula forg λμν (p), along the lines of T. Klein's original formula but much simpler, which shows that its expansion in powers ofp−1 has nonnegative coefficients.
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