Related papers: The $n$-Queens Problem in Higher Dimensions
As the dimension of a system increases, traditional methods for control and differential games rapidly become intractable, making the design of safe autonomous agents challenging in complex or team settings. Deep-learning approaches avoid…
How many chess rooks or queens does it take to guard all the squares of a given polyomino, the union of square tiles from a square grid? This question is a version of the art gallery problem in which the guards can "see" whichever squares…
Deep Neural Networks (DNNs) are powerful tools that have shown extraordinary results in many scenarios, ranging from pattern recognition to complex robotic problems. However, their intricate designs and lack of transparency raise safety…
Nowadays computational complexity of fast walsh hadamard transform and nonlinearity for Boolean functions and large substitution boxes is a major challenge of modern cryptography research on strengthening encryption schemes against linear…
We investigate distributed memory parallel sorting algorithms that scale to the largest available machines and are robust with respect to input size and distribution of the input elements. The main outcome is that four sorting algorithms…
We consider the task of secure multi-party distributed quantum computation on a quantum network. We propose a protocol based on quantum error correction which reduces the number of necessary qubits. That is, each of the $n$ nodes in our…
We are concerned with the fastest possible direct numerical solution algorithm for a thin-banded or tridiagonal linear system of dimension $N$ on a distributed computing network of $N$ nodes that is connected in a binary communication tree.…
Patients with motor control difficulties often "type" on a computer using a switch keyboard to guide a scanning cursor to text elements. We show how to optimize some parts of the design of switch keyboards by casting the design problem as…
Quantum computation represents a computational paradigm whose distinctive attributes confer the ability to devise algorithms with asymptotic performance levels significantly superior to those achievable via classical computation. Recent…
Packing a given sequence of items into as few bins as possible in an online fashion is a widely studied problem. We improve lower bounds for packing boxes into bins in two or more dimensions, both for general algorithms for squares and…
In recent years, the research community has discovered that deep neural networks (DNNs) and convolutional neural networks (CNNs) can yield higher accuracy than all previous solutions to a broad array of machine learning problems. To our…
A state vector-based quantum circuit simulation can provide accurate results for the development and validation of quantum computing algorithms, without being affected by noise interference. However, existing quantum circuit simulators have…
Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, d-Set Matching for integers d>2 is the problem of finding a matching of size…
In this paper we provide algorithms faster than O*(2^n) for several NP-complete domination-type problems. More precisely, we provide: an algorithm for CAPACITATED DOMINATING SET that solves it in O(1.89^n), a branch-and-reduce algorithm…
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.
Given a set $S$ of $n$ points in $\mathbb{R}^d$, the Closest Pair problem is to find a pair of distinct points in $S$ at minimum distance. When $d$ is constant, there are efficient algorithms that solve this problem, and fast approximate…
Decision making needs to take an uncertain environment into account. Over the last decades, robust optimization has emerged as a preeminent method to produce solutions that are immunized against uncertainty. The main focus in robust…
We study the query complexity of cake cutting and give lower and upper bounds for computing approximately envy-free, perfect, and equitable allocations with the minimum number of cuts. The lower bounds are tight for computing connected…
For a well-studied family of domination-type problems, in bounded-treewidth graphs, we investigate whether it is possible to find faster algorithms. For sets $\sigma,\rho$ of non-negative integers, a $(\sigma,\rho)$-set of a graph $G$ is a…
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…