We provide a Polynomial Time Approximation Scheme (PTAS) for the Bayesian optimal multiitem multi-bidder auction problem under two conditions. First, bidders are independent, have additive valuations and are from the same population. Second, every bidder’s value distributions of items are independent but not necessarily identical monotone hazard rate (MHR) distributions. For non-i.i.d. bidders,...

Diffusion is a fundamental graph process, underpinning such phenomena as epidemic disease contagion and the spread of innovation by word-of-mouth. We address the algorithmic problem of finding a set of k initial seed nodes in a network so that the expected size of the resulting cascade is maximized, under the standard independent cascade model of network diffusion. Runtime is a primary consider...

We consider the time optimal stabilization problem for a nonlinear control system ẋ = f(x, u). Let τ(y) be the minimum time needed to steer the system from the state y ∈ R to the origin, and call A(T ) the set of initial states that can be steered to the origin in time τ(y) ≤ T . Given any ε > 0, in this paper we construct a patchy feedback u = U(x) such that every solution of ẋ = f(x, U(x)), x...

While in general trading off exploration and exploitation in reinforcement learning is hard, under some formulations relatively simple solutions exist. Optimal decision thresholds for the multi-armed bandit problem, one for the infinite horizon discounted reward case and one for the finite horizon undiscounted reward case are derived, which make the link between the reward horizon, uncertainty ...

The harmonic solution (HS) on a graph is one of the most popular approaches to semi-supervised learning. This is the first paper that studies how to identify highly confident HS predictions on a graph based on the HS on its subgraph. The premise of our method is that the subgraph is much smaller than the graph and therefore the most confident predictions can be identified much faster than compu...

This paper studies the following online replacement problem. There is a real function f(t), called the ow rate, deened over a nite time horizon 0; T]. It is known that m f(t) M for some reals 0 m < M. At time 0 an online player starts to pay money at the rate f(0). At each time 0 < t T the player may changeover and continue paying money at the rate f(t). The complication is that each such chang...

A Las Vegas type probabilistic algorithm is presented for nding the Frobenius canonical form of an n n matrix T over any eld K. The algorithm requires O~(MM(n)) = MM(n) (logn) O(1) operations in K, where O(MM(n)) operations in K are suucient to multiply two n n matrices over K. This nearly matches the lower bound of (MM(n)) operations in K for this problem, and improves on the O(n 4) operations...

Given > 0, we compute a function taking prescribed values at N given points in R2, whose C2-norm is within a factor (1 + ) of least possible. The computation takes C( )N logN computer operations.

A hash function is a mapping from a key universe U to a range of integers, i.e., h : U/f0;1, . . . ,m 1g, where m is the range’s size. A perfect hash function for some set SDU is a hash function that is one-to-one on S, where mZ9S9. A minimal perfect hash function for some set SDU is a perfect hash function with a range of minimum size, combines theoretical analysis, practical performance, expe...