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 \(...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	arXiv.org
Hlavní autori:	Büchel, Alexander, Gilleßen, Ulrich, Kurt-Ulrich Witt
Médium:	Paper
Jazyk:	English
Vydavateľské údaje:	Ithaca Cornell University Library, arXiv.org 18.02.2019
Predmet:	Algorithms Integers Partitions
ISSN:	2331-8422
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Popis
Shrnutí:	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 \(T_j\).
Bibliografia:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1811.04014