• Corpus ID: 204904789

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

@article{Kreitzberg2019SelectionO,
title={Selection on \$X\_1+X\_2+\cdots + X\_m\$ with layer-ordered heaps},
author={Patrick Kreitzberg and Kyle A. Lucke and Oliver Serang},
journal={arXiv: Data Structures and Algorithms},
year={2019}
}
• Published 26 October 2019
• Computer Science
• arXiv: Data Structures and Algorithms
Selection on $X_1+X_2+\cdots + X_m$ is an important problem with many applications in areas such as max-convolution, max-product Bayesian inference, calculating most probable isotopes, and computing non-parametric test statistics, among others. Faster-than-naive approaches exist for $m=2$: Johnson \& Mizoguchi (1978) find the smallest $k$ values in $A+B$ with runtime $O(n \log(n))$. Frederickson \& Johnson (1982) created a method for finding the $k$ smallest values in $A+B$ with runtime $O(n… 2 Citations Figures and Tables from this paper Optimal construction of a layer-ordered heap • Computer Science ArXiv • 2020 A few algorithms for constructing LOHs are introduced, their complexity is analyzed, and it is demonstrated that one algorithm is optimal for building a LOH of any rank$\alpha$. Fast exact computation of the k most abundant isotope peaks with layer-ordered heaps • Computer Science Analytical chemistry • 2020 A novel algorithm for calculating the most abundant$k$isotopologue peaks of a compound is presented, which uses Serang's optimal method of selection on Cartesian products. References SHOWING 1-10 OF 16 REFERENCES Selection from heaps, row-sorted matrices and X+Y using soft heaps • Computer Science SOSA • 2019 A new optimal "output-sensitive" algorithm is obtained that performs only$O(m+\sum_{i=1}^m \log(k_i+1)$comparisons, where k_i$ is the number of items of the $i$-th list that belong to the overall set of~$k$ smallest items.
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