The paper sets lower bounds on envy-free divisions in cake-cutting problems.
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5 results for “envy-free”
problem Finding the minimum number of envy-free divisions in cake-cutting problems.
method Analyzes two scenarios: classical and hybrid, with different constraints and allocations.
result Sharp bounds and examples for envy-free divisions in both scenarios.
In classic fair division problems such as cake cutting and rent division, envy-freeness requires that each individual (weakly) prefer his allocation to anyone else's. On a conceptual level, we argue that envy-freeness also provides a compelling notion of fairness for classification tasks. Our technical focus is the gen…
Fairly allocate items with noisy queries, reducing envy.
problem Fairly allocate indivisible goods with unknown valuations.
method Use Gaussian noisy queries to find an envy-free allocation.
result The optimal number of queries scales as \( \frac{m^{2.5}}{Δ^2} \) for large negative-envy.
Algorithm allocates perishable resources online to minimize envy and inefficiency.
problem Online allocation of perishable resources to minimize envy and inefficiency.
method Algorithm uses predictions of perishing order and desired envy bound to adaptively allocate resources.
result Algorithm achieves optimal envy-efficiency trade-off as derived from strong lower bounds.
Proves existence of equivariant maps avoiding diagonal in n-space.
problem Existence of equivariant maps between spaces.
method Different approach to vanishing all obstructions.
result Vanishing of all equivariant obstructions.