O(1)-competitive algorithm for balanced markets on general metrics and distributions

Establish the existence of an O(1)-competitive online algorithm for the stochastic online metric matching problem in balanced markets on arbitrary metric spaces and arbitrary request distributions, where server locations are adversarially chosen and request locations are independently drawn from a known distribution. The goal is to achieve a constant competitive ratio with respect to the optimal offline matching cost for all general metrics and distributions.

Background

The paper develops a reduction showing that adversarial servers are no harder than stochastic servers and leverages this to obtain O(1)-competitive algorithms in several settings, including Euclidean spaces with smooth distributions for dimensions d ≥ 3. However, the results do not extend to all metrics and distributions. Prior work by Gupta et al. (2019) achieved an O((log log log n)^2)-competitive algorithm for general metrics and distributions, but a constant competitive ratio was not established in that generality.

The authors suggest two potential approaches: improving the analysis of Gupta et al.'s algorithm (which has no super-constant lower bound known) and applying their reduction with the SOAR algorithm to a simplified model. They note that a key barrier is characterizing OPT(n) for general metrics and distributions.