Optimizing the Envy Cycle Elimination Algorithm
For researchers in fair division, this work provides practical heuristics to enhance welfare in EF1 allocations, though the improvements are incremental.
The paper investigates heuristics for the envy cycle elimination algorithm to improve welfare guarantees in EF1 allocations, showing that jointly selecting the good and agent maximizing utility significantly reduces worst-case utilitarian welfare loss compared to the vanilla algorithm.
In the fair allocation of indivisible goods, a widely used notion of fairness is envy-freeness up to one good (EF1). A classical way to compute an EF1 allocation is the envy cycle elimination (ECE) algorithm, which iteratively assigns a good to an unenvied agent and, after each assignment, resolves any resulting envy cycle. Although the ECE algorithm always produces an EF1 allocation, it leaves considerable freedom in choosing both the next good to allocate and the agent to receive it. We investigate natural heuristics that exploit this flexibility to improve welfare guarantees. For example, we show that if the heuristic jointly selects the good and the receiving agent maximizing the utility, the worst-case utilitarian welfare loss is significantly lower than that of the vanilla algorithm. By contrast, restricting the heuristic to select only one of these two dimensions does not yield comparable improvements. We also complement our theoretical results with empirical average-case analysis.