Let S be a set of positive numbers and m an integer not less than 2. The problem is to partition S into m subsets such that the ratio of the largest subset sum to the smallest is as small as possible. Let ϱ g (S) be the value of this ratio using the greedy or largest-first rule and ϱ 0 (S) be the smallest possible value of this ratio, i.e., the optimal… (More)