In any optimal three-way partition, the numbers in any two of the subsets must be optimally partitioned two ways. More generally, if an optimal k-way partition includes a par- ticular subset, then optimally partitioning the numbers not in that subset k−1 ways will yieldy an optimal k-way partition.
This article explores algorithms for solving multi-way number-partitioning problems optimally. We explore previous algorithms as well as our own algorithms.
The NP-hard number-partitioning problem is to separate a multiset S of n positive integers into k subsets, such that the largest sum of the integers assigned ...
In computer science, multiway number partitioning is the problem of partitioning a multiset of numbers into a fixed number of subsets
The NP-hard number-partitioning problem is to separate a multiset S of n positive integers into k subsets such that the largest sum of the integers assigned ...
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Nov 26, 2024 · The problem is NP-hard, so you shouldn't expect any general algorithm that is always optimal, always works, and is efficient.
Apr 17, 2021 · The input is a set of n integers, and a fixed integer k. The required output is a partitioning of the integers into k subsets, such that the smallest sum of a ...
Jul 26, 2023 · In this paper, we design a fast parallel algorithm that finds an exact solution for the MWNP problem based on the recursive principle of optimality.
In this paper, we propose a new approach to multi-way number partitioning. Unlike previous algorithms, we con- sider the construction of potentially suboptimal ...
This thesis explores algorithms for solving multi-way number-partitioning problems optimally. ... We show experimentally that for high precision random problem ...