We show a lower bound of 1 + √2 for the approximation ratio of deterministic mechanisms and 2 for randomized mechanisms for knapsack, as well as the general monotone submodular functions.Expand

We show that a two-state anti-ferromagnetic spin system exhibits strong spatial mixing on all graphs of maximum degree at most Δ if and only if the system has a unique Gibbs measure.Expand

Budget feasible mechanism design studies procurement combinatorial auctions in which the sellers have private costs to produce items, and the buyer (auctioneer) aims to maximize a social valuation function on subsets of items, under the budget constraint.Expand

We study the stochastic combinatorial multi-armed bandit (CMAB) framework that allows a general nonlinear reward function, whose expected value may not depend only on the means of the input random variables but possibly on the entire distributions of these variables.Expand

We prove a complexity dichotomy theorem for the most general form of Boolean #CSP where every constraint function takes values in the field of complex numbers C.Expand

We design a deterministic fully polynomial-time approximation scheme (FPTAS) for counting the number of satisfying assignments for a given monotone CNF formula when each variable appears in at most 5 clauses.Expand