• Corpus ID: 220794047

# 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

## Figures from this paper

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## References

SHOWING 1-10 OF 10 REFERENCES
Optimal selection on X+Y simplified with layer-ordered heaps
A new optimal algorithm is presented, which uses layer-ordered heaps, which is both simple to implement and practically efficient.
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.
Fast exact computation of the k most abundant isotope peaks with layer-ordered heaps
• Chemistry, Computer Science
Analytical chemistry
• 2020
A novel algorithm for calculating the most abundant $k$ isotopologue peaks of a compound is presented, which uses Serang's optimal method of selection on Cartesian products.
A general method for solving divide-and-conquer recurrences
• Computer Science, Mathematics
SIGA
• 1980
A unifying method for solving recurrence relations of the form T(n) = kT(n/c) + f( n) is described that is both general in applicability and easy to apply.
On the Solution of Linear Recurrence Equations
• Computer Science
Comput. Optim. Appl.
• 1998
A new transform is defined - the Order transform - which has useful properties for providing asymptotic answers (compared to other transforms which supply exact answers) and helps in mapping the sequence under consideration to the two dimensional plane where the solution becomes easier to obtain.
Time Bounds for Selection
• Computer Science, Mathematics
J. Comput. Syst. Sci.
• 1973
The number of comparisons required to select the i-th smallest of n numbers is shown to be at most a linear function of n by analysis of a new selection algorithm-PICK. Specifically, no more than
Controlling the false discovery rate: a practical and powerful approach to multiple testing
• Mathematics
• 1995
SUMMARY The common approach to the multiplicity problem calls for controlling the familywise error rate (FWER). This approach, though, has faults, and we point out a few. A different approach to
Selection on X1
• Xm with layer-ordered heaps. arXiv preprint arXiv:1910.11993,
• 2019
and O
• Serang Selection on X1 + X2 + · · · + Xm with layer-ordered heaps, arXiv preprint arXiv:1910.11993,
• 2019
The soft heap: an approximate priority queue with optimal error rate
A simple variant of a priority queue, called a soft heap, is introduced, which is optimal for any value of ε in a comparison-based model and can be used to compute exact or approximate medians and percentiles optimally.