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arXiv · 2503.11107

Discrete Effort Distribution via Regret-enabled Greedy Algorithm

Song Cao·Taikun Zhu·Kai Jin
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Abstract

This paper addresses resource allocation problem with a separable objective function under a single linear constraint, formulated as maximizing $\sum_{j=1}^{n}R_j(x_j)$ subject to $\sum_{j=1}^{n}x_j=k$ and $x_j\in\{0,\dots,m\}$. While classical dynamic programming approach solves this problem in $O(n^2m^2)$ time, we propose a regret-enabled greedy algorithm that achieves $O(n\log n)$ time when $m=O(1)$. The algorithm significantly outperforms traditional dynamic programming for small $m$. Our algorithm actually solves the problem for all $k~(0\leq k\leq nm)$ in the mentioned time.

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Song Cao, Taikun Zhu, Kai Jin. 2025-03-14. Discrete Effort Distribution via Regret-enabled Greedy Algorithm. https://arxiv.org/abs/2503.11107

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