相关论文: Hunting Rabbits on the Hypercube

Lionel Levine's hat challenge has $t$ players, each with a (very large, or infinite) stack of hats on their head, each hat independently colored at random black or white. The players are allowed to coordinate before the random colors are…

We provide an algorithm to solve Rabin and Streett games over graphs with $n$ vertices, $m$ edges, and $k$ colours that runs in $\tilde{O}\left(mn(k!)^{1+o(1)} \right)$ time and $O(nk\log k \log n)$ space, where $\tilde{O}$ hides…

We study a family of graphs related to the $n$-cube. The middle cube graph of parameter $k$ is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube…

Task mapping in modern high performance parallel computers can be modeled as a graph embedding problem, which simulates the mapping as embedding one graph into another and try to find the minimum wirelength for the mapping. Though embedding…

The following general variant of deterministic Hats game is analyzed. Several sages wearing colored hats occupy the vertices of a graph, the $k$-th sage can have hats of one of $h(k)$ colors. Each sage tries to guess the color of his own…

Two-player graph games are a fundamental model for reasoning about the interaction of agents. These games are played between two players who move a token along a graph. In bidding games, the players have some monetary budget, and at each…

We study different domination problems of attacking and non-attacking rooks and queens on polyominoes and polycubes of all dimensions. Our main result proves that maximum independent domination is NP-complete for non-attacking queens and…

We study the localization game on dense random graphs. In this game, a {\em cop} $x$ tries to locate a {\em robber} $y$ by asking for the graph distance of $y$ from every vertex in a sequence of sets $W_1,W_2,\ldots,W_\ell$. We prove high…

For a given undirected graph $G$, an \emph{ordered} subset $S = {s_1,s_2,...,s_k} \subseteq V$ of vertices is a resolving set for the graph if the vertices of the graph are distinguishable by their vector of distances to the vertices in…

We apply our geometrical theory for counting placements of $q$ nonattacking on an $n\times n$ chessboard, from Parts~I and II, to partial queens: that is, chess pieces with any combination of horizontal, vertical, and $45^\circ$-diagonal…

While there has been tremendous activity in the area of statistical network inference on graphs, hypergraphs have not enjoyed the same attention, on account of their relative complexity and the lack of tractable statistical models. We…

This paper considers a problem of planning an attack in robotic football (RoboCup). The problem is reduced to finding a trajectory of the ball from its current position to the opponents goals. Heuristic search algorithm, i.e. A*, is used to…

The function that counts the number of ways to place nonattacking identical chess or fairy chess pieces in a rectangular strip of fixed height and variable width, as a function of the width, is a piecewise polynomial which is eventually a…

The optimal strategies to catch a randomly walking cat in various environments are presented. All games have a player that opens a box at step $i$. If the cat is in this box the player wins, if not, the cat moves randomly to an adjacent…

We study the parameterized complexity of dominating sets in geometric intersection graphs. In one dimension, we investigate intersection graphs induced by translates of a fixed pattern Q that consists of a finite number of intervals and a…

Classical random walks on finite graphs have an underrated property: a walk from any vertex can reach every other vertex in finite time, provided they are connected. Discrete-time quantum walks on finite connected graphs however, can have…

We study scattering quantum walks on highly symmetric graphs and use the walks to solve search problems on these graphs. The particle making the walk resides on the edges of the graph, and at each time step scatters at the vertices. All of…

A gambler moves on the vertices $1, \ldots, n$ of a graph using the probability distribution $p_{1}, \ldots, p_{n}$. A cop pursues the gambler on the graph, only being able to move between adjacent vertices. What is the expected number of…

Given a matching $M$ in the hypercube $Q^n$, the \emph{profile} of $M$ is the vector $\boldsymbol{x}=(x_1,\ldots, x_n) \in \mathbb{N}^n$ such that $M$ contains $x_i$ edges whose endpoints differ in the $i$th coordinate. If $M$ is a perfect…

We consider a four-player game on the discrete hypercube $Q_n = \{0,1\}^n$, where each of the four players has chosen a single vertex of the hypercube. Such a position is called a profile. Imagine there is a voter at every vertex, and each…