An output-sensitive Algorithm to partition a Sequence of Integers into Subsets with equal Sums

11/09/2018

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by   Alexander Büchel, et al.

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The well-known PARTITION problem: Given positive integers n, k and t such that t ≥ n and k · t = n+1 2, the algorithm partitions the elements of the set I_n = 1, ..., n into k mutually disjoint subsets T_j such that ∪_j=1^k T_j = I_n and ∑_x ∈ T_j x = t for each j ∈1,2, ..., k. The algorithm needs n ·n/2k + n(n+1)/2k steps to insert the n elements of I_n into the k sets T_j.