Fairness in Resource Allocation and Slowed-down Dependent Rounding

We consider an issue of much current concern: could fairness, an issue that is already difficult to guarantee, worsen when algorithms run much of our lives? We consider this in the context of resource-allocation problems; we show that algorithms can guarantee certain types of fairness in a verifiable way. Our conceptual contribution is a simple approach to fairness in this context, which only requires that all users trust some public lottery. Our technical contributions are in ways to address the $k$-center and knapsack-center problems that arise in this context: we develop a novel dependent-rounding technique that, via the new ingredients of "slowing down" and additional randomization, guarantees stronger correlation properties than known before.

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