Related papers: The $n$-Queens Problem in Higher Dimensions
From the 1970s up to now, Mastermind, a classic two-player game, has attracted plenty of attention, not only from the public as a popular game, but also from the academic community as a scientific issue. Mastermind with n positions and k…
We consider problems that can be solved by asking certain queries. The deterministic query complexity $D(P,n)$ of a problem $P$ is the smallest number of queries needed to ask in order to find the solution with an input of size $n$ (in the…
We initiate a systematic study of the time complexity of quantum divide and conquer algorithms for classical problems. We establish generic conditions under which search and minimization problems with classical divide and conquer algorithms…
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related…
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…
Using a bijective proof, we show the number of ways to arrange a maximum number of nonattacking pawns on a $2m\times 2m$ chessboard is ${2m\choose m}^2$, and more generally, the number of ways to arrange a maximum number of nonattacking…
A chessboard has the property that every row and every column has as many white squares as black squares. In this mostly methodological note, we address the problem of counting such rectangular arrays with a fixed (numeric) number of rows,…
We consider the problem of delivering content cached in a wireless network of n nodes randomly located on a square of area n. The network performance is described by the n2^n-dimensional caching capacity region of the wireless network. We…
The state vector-based simulation offers a convenient approach to developing and validating quantum algorithms with noise-free results. However, limited by the absence of cache-aware implementations and unpolished circuit optimizations, the…
We study the problem of computing the \textsc{Maxima} of a set of $n$ $d$-dimensional points. For dimensions 2 and 3, there are algorithms to solve the problem with order-oblivious instance-optimal running time. However, in higher…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
A sequence of vertices in a graph is called a legal dominating sequence if every vertex in the sequence dominates at least one vertex not dominated by those that precede it, and at the end all vertices of the graph are dominated. The Grundy…
We study online multidimensional variants of the generalized assignment problem which are used to model prominent real-world applications, such as the assignment of virtual machines with multiple resource requirements to physical…
The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…
We are studying $d$-dimensional geometric problems that have algorithms with $1-1/d$ appearing in the exponent of the running time, for example, in the form of $2^{n^{1-1/d}}$ or $n^{k^{1-1/d}}$. This means that these algorithms perform…
Noisy linear problems have been studied in various science and engineering disciplines. A class of "hard" noisy linear problems can be formulated as follows: Given a matrix $\hat{A}$ and a vector $\mathbf{b}$ constructed using a finite set…
A fundamental problem in quantum coding theory is to determine the maximum size of quantum codes of given block length and distance. A recent work introduced bounds based on semidefinite programming, strengthening the well-known quantum…
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…
A king in a directed graph is a node from which each node in the graph can be reached via paths of length at most two. There is a broad literature on tournaments (completely oriented digraphs), and it has been known for more than half a…
We consider Upper Domination, the problem of finding the minimal dominating set of maximum cardinality. Very few exact algorithms have been described for solving Upper Domination. In particular, no binary programming formulations for Upper…