Is anyone familiar with an algorithm that, given a set of integers, will choose a subset of items whose sum is closest to, but not greater than, a specified number? Basically I am looking to take a large set of data points and split it into the smallest number of subsets sums less than or equal to a specific number.The Government Printing Office (GPO) processes all sales and distribution of the CFR. For payment by credit card, call 202-512-1800, M-F, 8 a.m. to 4 p.m. e.s.t. or fax your order to 202-512-2250, 24 hours a day. For payment by check, write to the Superintendent of Documents, Attn: New Orders, P.O. Box 371954, Pittsburgh, PA 15250-7954.

i and each k-elements subset of X i has color c i. It may be useful to try to understand this theorem by checking small values of k;r; . In particular, for k= 1 it is just the Pigeonhole Principle. On the another hand, for k= 2, the 2-elements subsets of a set Xcan be seen as the edges of the complete graph whose vertices are the elements of X.

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