Related papers: Analysis of Divide & Conquer strategies for the 0-…
The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a…
Quantum optimization as a field has largely been restricted by the constraints of current quantum computing hardware, as limitations on size, performance, and fidelity mean most non-trivial problem instances won't fit on quantum devices.…
In the knapsack problem, we are given a knapsack of some capacity and a set of items, each with a size and a value. The goal is to pack a selection of these items fitting the knapsack that maximizes the total value. The online version of…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
Advances in information technology have led to extremely large datasets that are often kept in different storage centers. Existing statistical methods must be adapted to overcome the resulting computational obstacles while retaining…
Symbolic regression aims to find a function that best explains the relationship between independent variables and the objective value based on a given set of sample data. Genetic programming (GP) is usually considered as an appropriate…
Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also…
Computing sets of high quality solutions has gained increasing interest in recent years. In this paper, we investigate how to obtain sets of optimal solutions for the classical knapsack problem. We present an algorithm to count exactly the…
We describe a general strategy for sampling configurations from a given distribution, NOT based on the standard Metropolis (Markov chain) strategy. It uses the fact that nontrivial problems in statistical physics are high dimensional and…
We introduce a new Monte Carlo method by incorporating a guided distribution function to the conventional Monte Carlo method. In this way, the efficiency of Monte Carlo methods is drastically improved. To further speed up the algorithm, we…
We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of…
Computing optimal control policies for complex dynamical systems requires approximation methods to remain computationally tractable. Several approximation methods have been developed to tackle this problem. However, these methods do not…
By analogy with Monte Carlo algorithms, we propose new strategies for design and redesign of small molecule libraries in high-throughput experimentation, or combinatorial chemistry. Several Monte Carlo methods are examined, including…
Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…
A variant of the online knapsack problem is considered in the settings of trusted and untrusted predictions. In Unit Profit Knapsack, the items have unit profit, and it is easy to find an optimal solution offline: Pack as many of the…
We consider the 0-1 Incremental Knapsack Problem (IKP) where the capacity grows over time periods and if an item is placed in the knapsack in a certain period, it cannot be removed afterwards. The contribution of a packed item in each time…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
The divide-and-conquer framework, used extensively in classical algorithm design, recursively breaks a problem of size $n$ into smaller subproblems (say, $a$ copies of size $n/b$ each), along with some auxiliary work of cost…
Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC…
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…