  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.

Data Structures and Algorithms;Machine Learning;Combinatorics;Optimization and Control