Related papers: A Mathematical Foundation for the Numberlink Game
This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non-overlapping circles. The first half of the article is an exposition of…
Data analysis encompasses a spectrum of tasks, from high-level conceptual reasoning to lower-level execution. While AI-powered tools increasingly support execution tasks, there remains a need for intelligent assistance in conceptual tasks.…
We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…
Nonograms are a popular type of puzzle, where an arrangement of curves in the plane (in the classic version, a rectangular grid) is given together with a series of hints, indicating which cells of the subdivision are to be colored. The…
Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…
We propose a new class of game-theoretic models for network formation in which strategies are not directly related to edge choices, but instead correspond more generally to the exertion of social effort. The observed social network is thus…
Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to examine it within the context of Combinatorial Game Theory.…
Predicting edges in networks is a key problem in social network analysis and involves reasoning about the relationships between nodes based on the structural properties of a network. In particular, link prediction can be used to analyse how…
Without further ado, we present the P_3-game. The P_3-game is decidable for elementary classes of graphs such as paths and cycles. From an algorithmic point of view, the connected P_3-game is fascinating. We show that the connected P_3-game…
We investigate two types of query games played on a graph, pair queries and edge queries. We concentrate on investigating the two associated graph parameters for binomial random graphs, and showing that determining any of the two parameters…
Synchronous linear constraint system games are nonlocal games that verify whether or not two players share a solution to a given system of equations. Two algebraic objects associated to these games encode information about the existence of…
In the "Game about Squares" the task is to push unit squares on an integer lattice onto corresponding dots. A square can only be moved into one given direction. When a square is pushed onto a lattice point with an arrow the direction of the…
Parrondo's paradox is about a paradoxical game and gambling where two probabilistic losing games can be combined to form a winning game. While the counter intuitive game is interesting in itself, it can be thought of a discrete version of…
Motivated by the success of domination games and by a variation of the coloring game called the indicated coloring game, we introduce a version of domination games called the indicated domination game. It is played on an arbitrary graph $G$…
Markov chains are an important example for a course on stochastic processes because simple board games can be used to illustrate the fundamental concepts. For example, a looping board game (like Monopoly) consists of all recurrent states,…
We study two-player games with alternating moves played on infinite trees. Our main focus is on the case where the trees are full (regular) and the winning set is open (with respect to the product topology on the tree). Gale and Stewart…
Network Creation Games are a well-known approach for explaining and analyzing the structure, quality and dynamics of real-world networks like the Internet and other infrastructure networks which evolved via the interaction of selfish agents…
Recent years have witnessed the great success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks…
The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…
That there exist two losing games that can be combined, either by random mixture or by nonrandom alternation, to form a winning game is known as Parrondo's paradox. We establish a strong law of large numbers and a central limit theorem for…