Retaining more of the unweighted improvement in the weighted setting

Determine whether the weighted-resource algorithm can retain more of the competitive-ratio improvement achieved for unweighted reusable resources.

Background

The paper gives a black-box reduction from an unweighted competitive ratio greater than one half to a weighted ratio strictly greater than one half. Its explicit numerical guarantee is 0.500034, substantially smaller than the unweighted guarantee of approximately 0.511966. The authors leave unresolved whether a weighted algorithm or reduction can preserve more of the unweighted improvement.

References

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