Fair Division with Soft Conflicts

Researchers Hirotaka Yoneda and Masataka Yoneda have published a breakthrough paper titled 'Fair Division with Soft Conflicts' on arXiv, introducing a novel algorithmic solution to a complex resource allocation problem. The paper addresses how to fairly divide indivisible goods when there are 'soft' conflicts between items—represented as edges in a graph—where assigning conflicting goods to the same agent is allowed but undesirable. Their key contribution is a linear-time algorithm that, for any constant number of agents with general additive valuations, finds an allocation that is envy-free up to one good (EF1) while bounding the number of conflict violations. This solves a significant theoretical challenge in computational fair division, providing both efficiency and fairness guarantees where previous approaches struggled.

Technically, the algorithm achieves at most |E|/n + O(|E|^{1-1/(2n-2)}) violations, with the leading term |E|/n matching the worst-case lower bound. The researchers employ an innovative approach combining Biswas & Barman's (2018) algorithm for fair division with cardinality constraints with a new geometric 'closest points' argument. For the simpler case of identical additive valuations, they also present a straightforward round-robin-based algorithm that guarantees EF1 with at most |E|/n violations. This work advances the theoretical foundations of fair allocation with constraints and has immediate implications for practical applications requiring both fairness and conflict minimization in resource distribution systems.