Algorithmically Fair Maximization of Multiple Submodular Objective Functions
CoRR(2024)
摘要
Constrained maximization of submodular functions poses a central problem in
combinatorial optimization. In many realistic scenarios, a number of agents
need to maximize multiple submodular objectives over the same ground set. We
study such a setting, where the different solutions must be disjoint, and thus,
questions of fairness arise. Inspired from the fair division literature, we
suggest a simple round-robin protocol, where agents are allowed to build their
solutions one item at a time by taking turns. Unlike what is typical in fair
division, however, the prime goal here is to provide a fair algorithmic
environment; each agent is allowed to use any algorithm for constructing their
respective solutions. We show that just by following simple greedy policies,
agents have solid guarantees for both monotone and non-monotone objectives, and
for combinatorial constraints as general as p-systems (which capture
cardinality and matroid intersection constraints). In the monotone case, our
results include approximate EF1-type guarantees and their implications in fair
division may be of independent interest. Further, although following a greedy
policy may not be optimal in general, we show that consistently performing
better than that is computationally hard.
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