Optimizing the Envy Cycle Elimination Algorithm
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913179868594176 |
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| author | Celine, Karen Frilya Suksompong, Warut |
| author_facet | Celine, Karen Frilya Suksompong, Warut |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02233 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimizing the Envy Cycle Elimination Algorithm Celine, Karen Frilya Suksompong, Warut Computer Science and Game Theory 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. |
| title | Optimizing the Envy Cycle Elimination Algorithm |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2606.02233 |