  Given a set of numbers, the balanced partioning problem is to divide them
into two subsets, so that the sum of the numbers in each subset are as nearly
equal as possible, subject to the constraint that the cardinalities of the
subsets be within one of each other. We combine the balanced largest
differencing method (BLDM) and Korf's complete Karmarkar-Karp algorithm to get
a new algorithm that optimally solves the balanced partitioning problem. For
numbers with twelve significant digits or less, the algorithm can optimally
solve balanced partioning problems of arbitrary size in practice. For numbers
with greater precision, it first returns the BLDM solution, then continues to
find better solutions as time allows.
