Optimal PROP1 factor with exact maximum-item-value predictions

Determine the optimal PROP1 approximation factor achievable by online algorithms given exact maximum item value predictions.

Background

Exact maximum item value (MIV) predictions provide each agent’s maximum possible item value before the online allocation begins. The paper improves the previously known 1/n-PROP1 guarantee to 1/2-PROP1, and more generally to n/(n+κ) when each good is positively valued by at most κ agents.

The exact optimal dependence and constant factor remain unresolved: the paper establishes a constant guarantee but does not determine whether 1/2 is best possible or whether a larger factor can be achieved under exact MIV predictions.