# Optimal construction of a layer-ordered heap

@article{Pennington2020OptimalCO, title={Optimal construction of a layer-ordered heap}, author={Jake Pennington and Patrick Kreitzberg and Kyle A. Lucke and Oliver Serang}, journal={ArXiv}, year={2020}, volume={abs/2007.13356} }

The layer-ordered heap (LOH) is a simple, recently proposed data structure used in optimal selection on $X+Y$, thealgorithm with the best known runtime for selection on $X_1+X_2+\cdots+X_m$, and the fastest method in practice for computing the most abundant isotope peaks in a chemical compound. Here, we introduce a few algorithms for constructing LOHs, analyze their complexity, and demonstrate that one algorithm is optimal for building a LOH of any rank $\alpha$. These results are shown to…

## 4 Citations

Selection on $X_1+X_2+\cdots + X_m$ with layer-ordered heaps

- Mathematics, Computer Science
- 2019

The ``layer-ordered heap,'' a simple special class of heap with which a new, fast selection algorithm on the Cartesian product of arrays of length $n$ has runtime is introduced.

Optimally selecting the top k values from X + Y with layer-ordered heaps

- Computer Science, MedicinePeerJ Comput. Sci.
- 2021

A new algorithm is presented, which generates the top k values of the form Xi+Yj, which relies only on median-of-medians and is simple to implement and uses data structures contiguous in memory, cache efficient, and fast in practice.

Performing Selection on a Monotonic Function in Lieu of Sorting Using Layer-Ordered Heaps.

- Mathematics, MedicineJournal of proteome research
- 2021

A layer-ordering-based method for selection and partitioning on the transformed values, e.g., p values or q values, is introduced and used to partition peptides using an FDR threshold to speed up Percolator, a postprocessing algorithm used in mass-spectrometry-based proteomics to evaluate the quality of peptide-spectrum matches.

Selection on X1 + X2 + ⋯ + Xm via Cartesian product trees

- Medicine, Computer SciencePeerJ Comput. Sci.
- 2021

Performance of algorithms for selection on X1 + X2 + ⋯ + Xm are compared empirically, demonstrating the benefit of the algorithm proposed here.

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