Related papers: Approximation Theorems Related to the Coupon Colle…
The primal-dual scheme has been used to provide approximation algorithms for many problems. Goemans and Williamson gave a (2-1/(n-1))-approximation for the Prize-Collecting Steiner Tree Problem that runs in O(n^3 log n) time. it applies the…
In the "correlated sampling" problem, two players are given probability distributions $P$ and $Q$, respectively, over the same finite set, with access to shared randomness. Without any communication, the two players are each required to…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
We revisit a version of the classic occupancy scheme, where balls are thrown until almost all boxes receive a given number of balls. Special cases are widely known as coupon-collectors and dixie cup problems. We show that as the number of…
We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1, p_2, \ldots, p_s$, we design testers for the…
We present a 1.91457-approximation algorithm for the prize-collecting travelling salesman problem. This is obtained by combining a randomized variant of a rounding algorithm of Bienstock et al. and a primal-dual algorithm of Goemans and…
The classic Coupon-Collector Problem (CCP) is generalized to the extent that each coupons serves certain "purposes". Only basic probability theory is used. Centerpiece rather is an algorithm that efficiently counts all $k$-element…
Bounds of the accuracy of the normal approximation to the distribution of a sum of independent random variables are improved under relaxed moment conditions, in particular, under the absence of moments of orders higher than the second.…
We revisit the classic Pandora's Box (PB) problem under correlated distributions on the box values. Recent work of arXiv:1911.01632 obtained constant approximate algorithms for a restricted class of policies for the problem that visit boxes…
A typical polling system consists of a number of queues, attended by a single server in a fixed order. The vast majority of papers on polling systems focusses on Poisson arrivals, whereas very few results are available for general arrivals.…
Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson…
In this paper, we consider multistopping problems for finite discrete time sequences $X_1,...,X_n$. $m$-stops are allowed and the aim is to maximize the expected value of the best of these $m$ stops. The random variables are neither assumed…
Testing probabilistic programs is non-trivial due to their stochastic nature. Given an input, the program may produce different outcomes depending on the underlying stochastic choices in the program. This means testing the expected outcomes…
Based upon inequalities on Subset Probabilities, proofs of several conjectures on the Generalized Coupon Collector Problem (i.e. CCP with unequal popularity) are presented. Then we derive a very simple asymptotic relation between the…
In this paper, we first use the distribution of the number of records to demonstrate that the right tail probabilities of counts of rare events are generally better approximated by the right tail probabilities of Poisson distribution than…
In the hypothesis selection problem, we are given sample and query access to finite set of candidate distributions (hypotheses), $\mathcal{H} = \{H_1, \ldots, H_n\}$, and samples from an unknown distribution $P$, both over a domain…
We study several stochastic combinatorial problems, including the expected utility maximization problem, the stochastic knapsack problem and the stochastic bin packing problem. A common technical challenge in these problems is to optimize…
We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…