Submodular Approximation: Sampling-based Algorithms and Lower Bounds

Sequential Sampling Algorithms: Unified Analysis and Lower Bounds

Sequential sampling algorithms have recently attracted interest as a way to design scalable algorithms for Data mining and KDD processes. In this paper, we identify an elementary sequential sampling task (estimation from examples), from which one can derive many other tasks appearing in practice. We present a generic algorithm to solve this task and an analysis of its correctness and running ti...

Approximation Algorithms for Clustering Problems with Lower Bounds and Outliers

We consider clustering problems with non-uniform lower bounds and outliers, and obtain the first approximation guarantees for these problems. We have a setF of facilities with lower bounds {Li}i∈F and a setD of clients located in a common metric space {c(i, j)}i,j∈F∪D, and bounds k, m. A feasible solution is a pair ( S ⊆ F , σ : D 7→ S ∪ {out} ) , where σ specifies the client assignments, such ...

Sampling-based lower bounds for counting queries

It is well known that computing relative approximations of weighted counting queries such as the probability of evidence in a Bayesian network, the partition function of a Markov network, and the number of solutions of a constraint satisfaction problem is NP-hard. In this paper, we settle therefore on an easier problem of computing highconfidence lower bounds and propose an algorithm based on i...

Lower Bounds for Sampling Algorithms for Estimating the Average

We show lower bounds on the number of sample points and on the number of coin tosses used by general sampling algorithms for estimating the average value of functions over a large domain. The bounds depend on the desired precision and on the error probability of the estimate. Our lower bounds match upper bounds established by known algorithms, up to a mul-tiplicative constant. Furthermore, we g...

Lower Bounds and Approximation Guarantees