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Algorithms for Fair Allocations (AFFA)

Subject Area Theoretical Computer Science
Term from 2015 to 2023
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 284041127
 
Final Report Year 2024

Final Report Abstract

Overall, the research project “Algorithms for Fair Allocations” can be considered highly successful. This success is not only reflected in the large number of high-profile publications—where the extended project duration proved even advantageous for various reasons—but also in rather fundamental achievements. Our work played a significant role in establishing the methods of parameterized and multivariate complexity analysis in the field of fair resource distribution. These methods have proven to be very effective tools for a deeper understanding of the algorithmic complexity of typically NP-hard allocation problems. Moreover, by focusing on promising parameters and structural properties, they have contributed to conceptual enrichment of the research field beyond just algorithmic understanding. Numerous objectives described in the two proposals (initial and follow-up) were achieved. Some were realized by other research groups (partly before the start of the project), which naturally underscores the relevance and importance of the initiatives. The research location Germany, now also represented by TU Clausthal, has been able to further enhance its strong international visibility in the broad field of “Computational Social Choice.” Finally, some specific achievements within the project are highlighted: • In the area of “exclusive resource allocation,” we demonstrated that a theoretically demanding algorithmic framework (based on various forms of integer linear programming) not only leads to a theoretically very interesting efficient characterization but was also implemented and provided as a practically useful approach. Furthermore, our concept of envy-freeness in graphs has inspired numerous follow-up studies, allowing for a more realistic modeling of social relationships. • Among the many results and achievements in the area of “representative allocation,” the work on successive representatives and temporal preferences, as well as their robustness, seem to have the strongest resonance and the greatest potential for follow-up work. Generally, the temporal aspects in fair allocation, as introduced in this project, are now being considered in an increasing number of other related studies. • In the area of “shared resource allocation,” we consider the fundamental opening of research to these aspects as the most important achievement. We showed that even seemingly very minor or simple forms of sharing have non-trivial effects. For example, we demonstrated that sharing only a few resources between pairs of agents can be helpful in finding fairer solutions, but it is also sometimes computationally demanding. Additionally, donating resources, which essentially corresponds to not allocating some resources, proved to be a fruitful concept and highlights the previously much-neglected “partial allocations.”

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