Related papers: Lower bound of computational complexity of knapsac…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter…
A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear…
The stochastic knapsack problem is the stochastic variant of the classical knapsack problem in which the algorithm designer is given a a knapsack with a given capacity and a collection of items where each item is associated with a profit…
In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by the smallest signal strength that it can…
We introduce the quadratic balanced optimization problem (QBOP) which can be used to model equitable distribution of resources with pairwise interaction. QBOP is strongly NP-hard even if the family of feasible solutions has a very simple…
We study nonequilibrium quantum dynamics of spin chains by employing principal component analysis (PCA) on data sets of wave function snapshots and examine how information propagates within these data sets. The quantities we employ are…
We prove new lower bounds for suitable competitive ratio measures of two relaxed online packing problems: online removable multiple knapsack, and a recently introduced online minimum peak appointment scheduling problem. The high level…
This paper studies the complexity for finding approximate stationary points of nonconvex-strongly-concave (NC-SC) smooth minimax problems, in both general and averaged smooth finite-sum settings. We establish nontrivial lower complexity…
In this paper, we address two minimal controllability problems, where the goal is to determine a minimal subset of state variables in a linear time-invariant system to be actuated to ensure controllability under additional constraints.…
We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and powerful ways of rounding.…
We study the computational complexity of a very basic problem, namely that of finding solutions to a very large set of random linear equations in a finite Galois Field modulo q. Using tools from statistical mechanics we are able to identify…
Today, hardware constraints are an important limitation on quantum adiabatic optimization algorithms. Firstly, computational problems must be formulated as quadratic unconstrained binary optimization (QUBO) in the presence of noisy coupling…
Submodular maximization is a classic algorithmic problem with multiple applications in data mining and machine learning; there, the growing need to deal with massive instances motivates the design of algorithms balancing the quality of the…
Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…
Determining properties of ground states of spin Hamiltonians remains a topic of central relevance connecting disciplines of mathematical, theoretical and applied physics. In the last few decades, ground state properties of physical systems…
Generalizing work of K\"unnemann, Paturi, and Schneider [ICALP 2017], we study a wide class of high-dimensional dynamic programming (DP) problems in which one must find the shortest path between two points in a high-dimensional grid given a…
Commonly used in computer vision and other applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into…
Clustering problems are fundamental to unsupervised learning. There is an increased emphasis on fairness in machine learning and AI; one representative notion of fairness is that no single demographic group should be over-represented among…
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…