Tight competitive ratio of the random-priority algorithm

Determine the tight competitive ratio of the random-priority highest-priority-available-resource algorithm for reusable resources, even when all usage durations are identical deterministic constants.

Background

The paper establishes that the random-priority algorithm beats a competitive ratio of one half for unweighted reusable resources with resource-dependent i.i.d. stochastic durations, obtaining a ratio of approximately 0.511966. This result also covers heterogeneous deterministic durations as a special case. The nonreusable setting provides an upper bound of 1-1/e, but the gap between this upper bound and the paper’s guarantee remains unresolved, including in the simpler common-deterministic-duration setting.

References

For future works, the main open question is to determine the tight competitive ratio of for reusable resources, even when all durations are the same deterministic constant.

— Beating One Half for Online Bipartite Matching with Reusable Resources  (2610.01993 - Bei et al., 1 Oct 2026) in Section Discussion

For weighted resources, it remains open whether one can retain more of the unweighted improvement and whether a guarantee above $1/2$ is possible without sampling access to the duration distributions.

— Beating One Half for Online Bipartite Matching with Reusable Resources  (2610.01993 - Bei et al., 1 Oct 2026) in Section Discussion