Related papers: Stability and Complexity of Minimising Probabilist…
We give algorithms for the optimization problem: $\max_\rho \ip{Q}{\rho}$, where $Q$ is a Hermitian matrix, and the variable $\rho$ is a bipartite {\em separable} quantum state. This problem lies at the heart of several problems in quantum…
The problem of maximizing weighted sum rates in the downlink of a multicell environment is of considerable interest. Unfortunately, this problem is known to be NP-hard. For the case of multi-antenna base stations and single antenna mobile…
This paper considers a distributed stochastic optimization problem where the goal is to minimize the time average of a cost function subject to a set of constraints on the time averages of a related stochastic processes called penalties. We…
The minimum and maximum cuts of an undirected edge-weighted graph are classic problems in graph theory. While the Min-Cut Problem can be solved in P, the Max-Cut Problem is NP-Complete. Exact and heuristic methods have been developed for…
We introduce the notion of a stable instance for a discrete optimization problem, and argue that in many practical situations only sufficiently stable instances are of interest. The question then arises whether stable instances of NP--hard…
Approximate algorithms for structured prediction problems---such as LP relaxations and the popular alpha-expansion algorithm (Boykov et al. 2001)---typically far exceed their theoretical performance guarantees on real-world instances. These…
Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on…
We present novel minibatch stochastic optimization methods for empirical risk minimization problems, the methods efficiently leverage variance reduced first-order and sub-sampled higher-order information to accelerate the convergence speed.…
The computational complexity of the partition, 0-1 subset sum, unbounded subset sum, 0-1 knapsack and unbounded knapsack problems and their multiple variants were studied in numerous papers in the past where all the weights and profits were…
Clustering under most popular objective functions is NP-hard, even to approximate well, and so unlikely to be efficiently solvable in the worst case. Recently, Bilu and Linial \cite{Bilu09} suggested an approach aimed at bypassing this…
Finite-state tree automata are a well studied formalism for representing term languages. This paper studies the problem of determining the regularity of the set of instances of a finite set of terms with variables, where each variable is…
Threshold automata are a formalism for modeling and analyzing fault-tolerant distributed algorithms, recently introduced by Konnov, Veith, and Widder, describing protocols executed by a fixed but arbitrary number of processes. We conduct…
In the constrained synchronization problem we ask if a given automaton admits a synchronizing word coming from a fixed regular constraint language. We show that intersecting a given constraint language with an ideal language decreases the…
Minimum vertex cover problem is an NP-Hard problem with the aim of finding minimum number of vertices to cover graph. In this paper, a learning automaton based algorithm is proposed to find minimum vertex cover in graph. In the proposed…
We propose and analyze a stabilizing iteration scheme for the algorithmic implementation of model predictive control for linear discrete-time systems. Polytopic input and state constraints are considered and handled by means of so-called…
When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the…
We give simple deterministic reductions demonstrating the NP-hardness of approximating the nearest codeword problem and minimum distance problem within arbitrary constant factors (and almost-polynomial factors assuming NP cannot be solved…
Despite much research, hard weighted problems still resist super-polynomial improvements over their textbook solution. On the other hand, the unweighted versions of these problems have recently witnessed the sought-after speedups.…
We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new…
We study a scheduling problem in which jobs may be split into parts, where the parts of a split job may be processed simultaneously on more than one machine. Each part of a job requires a setup time, however, on the machine where the job…