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

We present a polynomial time algorithm, which solves a nonstandard Variation of the well-known PARTITION-problem: Given positive integers \(n, k\) and \(t\) such that \(t \geq n\) and \(k \cdot t = {n+1 \choose 2}\), the algorithm partitions the elements of the set \(I_n = \{1, \ldots, n\}\) into \(...

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Veröffentlicht in:	arXiv.org
Hauptverfasser:	Büchel, Alexander, Gilleßen, Ulrich, Kurt-Ulrich Witt
Format:	Paper
Sprache:	Englisch
Veröffentlicht:	Ithaca Cornell University Library, arXiv.org 18.02.2019
Schlagworte:	Algorithms Integers Partitions
ISSN:	2331-8422
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We present a polynomial time algorithm, which solves a nonstandard Variation of the well-known PARTITION-problem: Given positive integers \(n, k\) and \(t\) such that \(t \geq n\) and \(k \cdot t = {n+1 \choose 2}\), the algorithm partitions the elements of the set \(I_n = \{1, \ldots, n\}\) into \(k\) mutually disjoint subsets \(T_j\) such that \(\cup_{j=1}^k T_j = I_n\) and \(\sum_{x \in T_{j}} x = t\) for each \(j \in \{1,2, \ldots, k\}\). The algorithm needs \(\mathcal{O}(n \cdot ( \frac{n}{2k} + \log \frac{n(n+1)}{2k} ))\) steps to insert the \(n\) elements of \(I_n\) into the \(k\) sets \(T_j\).
Bibliographie:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1811.04014