A Quadratic Time Locally Optimal Algorithm for NP-hard Equal Cardinality Partition Optimization
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Abstract (arXiv)
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(N2) 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.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 5 of its 54 references that are in the map. First posted on arXiv 16 Sep 2021.
Builds on
5 of 54 references.
References · 5
- 2021Generalized Huber Loss for Robust Learning and its Efficient Minimization for a Robust Statisticscited by 32
- 2021Optimally Efficient Sequential Calibration of Binary Classifiers to Minimize Classification Errorcited by 17
- 2018Fair Division Under Cardinality Constraintscited by 10
- 2021Optimal and Efficient Algorithms for General Mixable Losses against Switching Oraclescited by 10
- 2021Efficient Locally Optimal Number Set Partitioning for Scheduling, Allocation and Fair Selectioncited by 4
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Citing papers per year: 2022: 2; 2023: 1.
3 papers.