Given a set of items and a collection of players, each with a nonnegative monotone valuation set function over the items,
the welfare maximization problem requires that every item be allocated to exactly one player,
and one wishes to maximize the sum of values obtained by the players,
as computed ... more >>>

In this work, we study the space complexity of sketching the intersection profile of a distribution $D$ on $2^{[n]}$. Specifically, we seek a succinct data structure that, for any query set $S \subseteq [n]$, approximates the quantity $\Pr_{T \sim D}[T \cap S \neq \emptyset]$ to within a small constant additive ... more >>>