Related papers: Solving the n-Queens Problem in Higher Dimensions
We analyze integer linear programs which we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness…
Advantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known…
We consider a multi-class queueing model of a telephone call center, in which a system manager dynamically allocates available servers to customer calls. Calls can terminate through either service completion or customer abandonment, and the…
We describe scalable protocols for solving the secure multi-party computation (MPC) problem among a large number of parties. We consider both the synchronous and the asynchronous communication models. In the synchronous setting, our…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
The prevailing view is that quantum phenomena can be harnessed to tackle certain problems beyond the reach of classical approaches. Quantifying this capability as a quantum-classical separation and demonstrating it on current quantum…
In [1] the authors studied the closed tour problem on the $8\times 8$ chessboard of a chess piece, called $k$-prince, leaving open the existence of such a tour when $k=7$. In this note we find a solution to this open case.
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
We prove that king chasing problem in Chinese Chess is NP-hard when generalized to $n\times n$ boards. `King chasing' is a frequently-used strategy in Chinese Chess, which means that the player has to continuously check the opponent in…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear…
The Mean King's problem with mutually unbiased bases is reconsidered for arbitrary d-level systems. Hayashi, Horibe and Hashimoto [Phys. Rev. A 71, 052331 (2005)] related the problem to the existence of a maximal set of d-1 mutually…
Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum…
We consider the classic problem of fairly dividing a heterogeneous good ("cake") among several agents with different valuations. Classic cake-cutting procedures either allocate each agent a collection of disconnected pieces, or assume that…
This paper assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
In this paper we consider what can be computed by a user interacting with a potentially malicious server, when the server performs polynomial-time quantum computation but the user can only perform polynomial-time classical (i.e.,…
Solving hard problems is one of the most important issues in computing to be addressed by a quantum computer. Previously, we have shown that the H-SEARCH; which is the problem of finding a Hadamard matrix (H-matrix) among all possible…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
Most cloud services and distributed applications rely on hashing algorithms that allow dynamic scaling of a robust and efficient hash table. Examples include AWS, Google Cloud and BitTorrent. Consistent and rendezvous hashing are algorithms…