  An algorithm for number-partitioning is called value-monotone if whenever one
of the input numbers increases, the objective function (the largest sum or the
smallest sum of a subset in the output) weakly increases. This note proves that
the List Scheduling algorithm and the Longest Processing Time algorithm are
both value-monotone. This is in contrast to another algorithm -- MultiFit --
which is not value-monotone.

Data Structures and Algorithms