Multi-way number partitioning using weakest link optimality

A method of optimally assigning a plurality of programming tasks to a plurality of processors using multi-way partitioning of a set of positive numbers representing processing costs for the plurality of programming tasks comprising:

• establishing a first partition for a pairwise decomposition of the set wherein the first partition has a first candidate subset of the numbers, by executing first instructions in a computer system;
• setting a lower cost bound equal to a maximum cost of the first candidate subset according to an objective function, by executing second instructions in the computer system;
• recursively generating second partitions for the pairwise decomposition wherein each second partition has a plurality of second candidate subsets of the numbers, by executing third instructions in the computer system;
• determining that each second candidate subset in a selected one of the second partitions has a cost according to the objective function which is less than or equal to the lower cost bound, by executing fourth instructions in the computer system;
• responsive to said determining, returning the first partition with the selected second partition as an optimal solution regardless of whether the selected second partition is an optimal decomposition, by executing fifth instructions in the computer system;
• and
• assigning the plurality of programming tasks to the plurality of processors according to the optimal solution, by executing sixth instructions in the computer system.