  One of the most important processing steps in any analysis pipeline is
handling missing data. Traditional approaches simply delete any sample or
feature with missing elements. Recent imputation methods replace missing data
based on assumed relationships between observed data and the missing elements.
However, there is a largely under-explored alternative amid these extremes.
Partial deletion approaches remove excessive amounts of missing data, as
defined by the user. They can be used in place of traditional deletion or as a
precursor to imputation. In this manuscript, we expand upon the Mr. Clean suite
of algorithms, focusing on the scenario where all missing data is removed. We
show that the RowCol Integer Program can be recast as a Linear Program, thereby
reducing runtime. Additionally, the Element Integer Program can be reformulated
to reduce the number of variables and allow for high levels of parallelization.
Using real-world data sets from genetic, gene expression, and single cell
RNA-seq experiments we demonstrate that our algorithms outperform existing
deletion techniques over several missingness values, balancing runtime and data
retention. Our combined greedy algorithm retains the maximum number of valid
elements in 126 of 150 scenarios and stays within 1\% of maximum in 23 of the
remaining experiments. The reformulated Element IP complements the greedy
algorithm when removing all missing data, boasting a reduced runtime and
increase in valid elements in larger data sets, over its generic counterpart.
These two programs greatly increase the amount of valid data retained over
traditional deletion techniques and further improve on existing partial
deletion algorithms.
