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Computer Science > Data Structures and Algorithms

arXiv:2109.07882 (cs)
[Submitted on 16 Sep 2021]

Title:A Quadratic Time Locally Optimal Algorithm for NP-hard Equal Cardinality Partition Optimization

Authors:Kaan Gokcesu, Hakan Gokcesu
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Abstract:We study the optimization version of the equal cardinality set partition problem (where the absolute difference between the equal sized partitions' sums are minimized). While this problem is NP-hard and requires exponential complexity to solve in general, we have formulated a weaker version of this NP-hard problem, where the goal is to find a locally optimal solution. The local optimality considered in our work is under any swap between the opposing partitions' element pairs. To this end, we designed an algorithm which can produce such a locally optimal solution in $O(N^2)$ time and $O(N)$ space. Our approach does not require positive or integer inputs and works equally well under arbitrary input precisions. Thus, it is widely applicable in different problem scenarios.
Subjects: Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG); Combinatorics (math.CO); Optimization and Control (math.OC)
Cite as: arXiv:2109.07882 [cs.DS]
  (or arXiv:2109.07882v1 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.2109.07882

Submission history

From: Kaan Gokcesu [view email]
[v1] Thu, 16 Sep 2021 11:25:18 UTC (13 KB)
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