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arXiv · 2008.07023

Selection on $X_1 + X_1 + \cdots X_m$ via Cartesian product tree

Patrick Kreitzberg·Kyle Lucke·Jake Pennington·Oliver Serang
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Abstract

Selection on the Cartesian product is a classic problem in computer science. Recently, an optimal algorithm for selection on $X+Y$, based on soft heaps, was introduced. By combining this approach with layer-ordered heaps (LOHs), an algorithm using a balanced binary tree of $X+Y$ selections was proposed to perform $k$-selection on $X_1+X_2+\cdots+X_m$ in $o(n\cdot m + k\cdot m)$, where $X_i$ have length $n$. Here, that $o(n\cdot m + k\cdot m)$ algorithm is combined with a novel, optimal LOH-based algorithm for selection on $X+Y$ (without a soft heap). Performance of algorithms for selection on $X_1+X_2+\cdots+X_m$ are compared empirically, demonstrating the benefit of the algorithm proposed here.

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Patrick Kreitzberg, Kyle Lucke, Jake Pennington, Oliver Serang. 2020-08-16. Selection on $X_1 + X_1 + \cdots X_m$ via Cartesian product tree. https://arxiv.org/abs/2008.07023

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