Related papers: On a generalisation of the coupon collector proble…
A conditional sampling oracle for a probability distribution D returns samples from the conditional distribution of D restricted to a specified subset of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et al. 2014)…
We show the first unconditional pseudo-determinism result for all of search-BPP. Specifically, we show that every BPP search problem can be computed pseudo-deterministically on average for infinitely many input lengths. In other words, for…
To reduce computational complexity and delay in randomized network coded content distribution, and for some other practical reasons, coding is not performed simultaneously over all content blocks, but over much smaller, possibly overlapping…
Given a random process $x(\tau)$ which undergoes stochastic resetting at a constant rate $r$ to a position drawn from a distribution ${\cal P}(x)$, we consider a sequence of dynamical observables $A_1, \dots, A_n$ associated to the…
A lossy source code $\mathcal{C}$ with rate $R$ for a discrete memoryless source $S$ is called subset-universal if for every $0<R'< R$, almost every subset of $2^{nR'}$ of its codewords achieves average distortion close to the source's…
Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized…
We derive a recursive formula for the moments of the number of flips using a possibly biased coin to produce a prescribed finite binary string $S$ when $S$ is either a run of heads or a run of heads followed by a tails. Our recursive…
The random cost problem is the problem of finding the minimum in an exponentially long list of random numbers. By definition, this problem cannot be solved faster than by exhaustive search. It is shown that a classical NP-hard optimization…
We consider the problem of choosing the best of $n$ samples, out of a large random pool, when the sampling of each member is associated with a certain cost. The quality (worth) of the best sample clearly increases with $n$, but so do the…
The Chow-Robbins game is a classical still partly unsolved stopping problem introduced by Chow and Robbins in 1965. You repeatedly toss a fair coin. After each toss, you decide if you take the fraction of heads up to now as a payoff,…
We introduce new definitions of universal and superuniversal computable codes, which are based on a code's ability to approximate Kolmogorov complexity within the prescribed margin for all individual sequences from a given set. Such sets of…
It is known that, by accounting for the multiboson interferences up to a finite order, the output distribution of noisy Boson Sampling, with distinguishability of bosons serving as noise, can be approximately sampled from in a time…
Superquadrics provide a compact representation of common shapes and have been used both for object/surface modelling in computer graphics and as object-part representation in computer vision and robotics. Superquadrics refer to a family of…
We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a…
In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets $X_m$ of the set $X_n$ (subset sum problem). Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly…
In this research, we study the problem that a collector acquires items from the owner based on the item qualities the owner declares and an independent appraiser's assessments. The owner is interested in maximizing the probability that the…
We consider large uniform labeled random graphs in different classes with prescribed decorations in their modular decomposition. Our main result is the estimation of the number of copies of every graph as an induced subgraph. As a…
We consider the following two deterministic inventory optimization problems over a finite planning horizon $T$ with non-stationary demands. (a) Submodular Joint Replenishment Problem: This involves multiple item types and a single retailer…
Quantum machine learning (QML) aims to accelerate machine learning tasks by exploiting quantum computation. Previous work studied a QML algorithm for selecting sparse subnetworks from large shallow neural networks. Instead of directly…
We consider the count of subgraphs with an arbitrary configuration of endpoints in the random-connection model based on a Poisson point process on ${\Bbb R}^d$. We present combinatorial expressions for the computation of the cumulants and…