相关论文: The $n$-queens completion problem

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,…

This exploratory paper considers the notion of a covering of a configuration and $G$-coverings which are coverings that are quotients under a semi-regular group action. We consider prime configurations, those which cannot $G$-cover other…

In recent work Simkin shows that bounds on an exponent occurring in the famous $n$-queens problem can be evaluated by solving convex optimization problems, allowing him to find bounds far tighter than previously known. In this note we use…

Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such…

Provisioning is a technique for avoiding repeated expensive computations in what-if analysis. Given a query, an analyst formulates $k$ hypotheticals, each retaining some of the tuples of a database instance, possibly overlapping, and she…

The dimension of a partial order $P$ is the minimum number of linear orders whose intersection is $P$. There are efficient algorithms to test if a partial order has dimension at most $2$. In 1982 Yannakakis showed that for $k\geq 3$ to test…

The low-rank matrix completion problem asks whether a given real matrix with missing values can be completed so that the resulting matrix has low rank or is close to a low-rank matrix. The completed matrix is often required to satisfy…

Checking whether a system of linear equations is consistent is a basic computational problem with ubiquitous applications. When dealing with inconsistent systems, one may seek an assignment that minimizes the number of unsatisfied…

The Parks Puzzle is a paper-and-pencil puzzle game that is classically played on a square grid with different colored regions (the parks). The player needs to place a certain number of "trees" in each row, column, and park such that none…

Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not…

The problem of existence of closed knight tours for rectangular chessboards was solved by Schwenk in 1991. Last year, in 2011, DeMaio and Mathew provide an extension of this result for 3-dimensional rectangular boards. In this article, we…

We study the problem of generating a test sequence that achieves maximal coverage for a reactive system under test. We formulate the problem as a repeated game between the tester and the system, where the system state space is partitioned…

We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…

We study the domination number $\gamma(Q_n^3)$ of the three-dimensional $n \times n \times n$ queen graph. The main result is a stratified theorem computing, for each position type -- corner, edge, face, or interior -- the number of…

We study the problem of connecting the parts of a multipartite graph using a minimum number of edges under a matching constraint. We introduce interconnection trees, defined as matchings whose projections onto the quotient graph form a…

A conjecture of Fan and Raspaud [3] asserts that every bridgeless cubic graph con-tains three perfect matchings with empty intersection. Kaiser and Raspaud [6] sug-gested a possible approach to this problem based on the concept of a…

The existence of universal quantum computers has been theoretically well established. However, building up a real quantum computer system not only relies on the theory of universality, but also needs methods to satisfy requirements on other…

A complete graph is the graph in which every two vertices are adjacent. For a graph $G=(V,E)$, the complete width of $G$ is the minimum $k$ such that there exist $k$ independent sets $\mathtt{N}_i\subseteq V$, $1\le i\le k$, such that the…

Let $G$ be a complete edge-weighted graph on $n$ vertices. To each subset of vertices of $G$ assign the cost of the minimum spanning tree of the subset as its weight. Suppose that $n$ is a multiple of some fixed positive integer $k$. The…

This paper investigates a partially observable queueing system with $N$ nodes in which each node has a dedicated arrival stream. There is an extra arrival stream to balance the load of the system by routing its customers to the shortest…