Multi-Way Number Partitioning: an Information-Theoretic View

Abstract: The number partitioning problem is the problem of partitioning a given list of numbers into multiple subsets so that the sum of the numbers in each subset are as nearly equal as possible. We introduce two closely related notions of the "most informative" and "most compressible" partitions. Most informative partitions satisfy a principle of optimality property. We also give an exact algorithm (based on Huffman coding) with a running time of O(nlog(n)) in input size n to find the most compressible partition.