A new research paper explores the conditions under which fair division of indivisible goods can be achieved while satisfying both envy-freeness up to one good (EF1) and Pareto optimality (PO). The study identifies that for two agents, exactly seven goods are sufficient to guarantee an EF1 and PO allocation when valuations are strictly increasing. However, with eight goods, an instance can be constructed where every EF1 allocation is Pareto dominated, establishing eight as the necessary threshold for a counterexample. The research also extends existing findings on the computational complexity of this problem, showing it remains NP-hard even under specific constraints for normalized, integer-valued, monotone submodular valuations. AI
IMPACT Niche theoretical computer science research with minimal direct impact on AI operations.
RANK_REASON Academic paper published on arXiv detailing theoretical computer science research. [lever_c_demoted from research: ic=1 ai=0.1]
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