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

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

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 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 deterministic fully polynomial-time approximation scheme (FPTAS) for computing the partition function for a class of multi-spin systems, extending the known approximable regime by an exponential scale.Expand