Power laws and power-of-two-choices
This work addresses a theoretical problem in allocation algorithms, offering incremental insights by modifying a classical approach.
The paper investigates a variation of the 'power of two choices' allocation algorithm by selecting the largest instead of the smallest of d randomly-chosen options, resulting in a power-law-like distribution where the i-th smallest value scales with i^(d-1) with high probability, and provides formulas for expectation and concentration.
This paper analyzes a variation on the well-known "power of two choices" allocation algorithms. Classically, the smallest of $d$ randomly-chosen options is selected. We investigate what happens when the largest of $d$ randomly-chosen options is selected. This process generates a power-law-like distribution: the $i^{th}$-smallest value scales with $i^{d-1}$, where $d$ is the number of randomly-chosen options, with high probability. We give a formula for the expectation and show the distribution is concentrated around the expectation