Buffers unlock fair division in online allocation of mixed-value items

A team of computer scientists (Amanatidis, Giaconi, Markakis, Protopapas) has tackled one of the hardest problems in algorithmic fairness: dividing items with mixed positive and negative values as they arrive one by one, without knowing future items. In their paper "Online Fair Division Meets Reordering Buffers" (arXiv:2607.01159), they show that a modest buffer—limited to storing a few items—allows algorithms to guarantee strong fairness properties. Specifically, for instances where each agent assigns at most k distinct values to items, a buffer of size O(k·n) (where n is the number of agents) enables an allocation that is envy-free up to one item (EF1) at every time step and fully EF at most steps. The approach constructs a sequence of envy-free matchings that allocate the majority of items, using novel combinatorial arguments.

The result is significant because the fully online version of this problem (no buffer) has strong impossibility results—fairness is almost impossible without future knowledge. By allowing a small buffer, the authors create a natural interpolation between online and offline settings. They also extend their findings to general additive valuations, with a dependence on the largest ratio between two values of the same sign for any agent. The paper includes impossibility results showing that smaller buffers cannot achieve such guarantees, establishing tight boundaries. This work has practical implications for cloud resource allocation, task scheduling in multi-agent systems, and any domain where items (or jobs) with varying utilities must be assigned fairly in real-time.