Related papers: A Mathematical Foundation for the Numberlink Game
In this paper, we consider a game played on a rectangular $m \times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along…
A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships…
Mathematical text is written using a combination of words and mathematical expressions. This combination, along with a specific way of structuring sentences makes it challenging for state-of-art NLP tools to understand and reason on top of…
We consider the problem of link prediction in networks whose edge structure may vary (sufficiently slowly) over time. This problem, with applications in many important areas including social networks, has two main variants: the first, known…
We consider the generalized game Lights Out played on a graph and investigate the following question: for a given positive integer $n$, what is the probability that a graph chosen uniformly at random from the set of graphs with $n$ vertices…
Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…
Many forcing notions obtained using the creature technology are naturally connected with certain integer games.
Matching games naturally generalize assignment games, a well-known class of cooperative games. Interest in matching games has grown recently due to some breakthrough results and new applications. This state-of-the-art survey provides an…
Recall the classical 15-puzzle, consisting of 15 sliding blocks in a $4\times 4$ grid. Famously, the configuration space of this puzzle consists of two connected components, corresponding to the odd and even permutations of the symmetric…
MathLink is Wolfram Research's protocol for communicating with the Mathematica Kernel and is used extensively in their own Notebook Frontends. The Mathematica Book insinuates that linking C programs with MathLink is straightforward but in…
The Connections puzzle is a word association game published daily by The New York Times (NYT). In this game, players are asked to find groups of four words that are connected by a common theme. While solving a given Connections puzzle…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
We study the algorithmic aspect of edge bundling. A bundled crossing in a drawing of a graph is a group of crossings between two sets of parallel edges. The bundled crossing number is the minimum number of bundled crossings that group all…
Solving crossword puzzles requires diverse reasoning capabilities, access to a vast amount of knowledge about language and the world, and the ability to satisfy the constraints imposed by the structure of the puzzle. In this work, we…
The simple connected graphs may be classified by their cycle composition (number and lengths of cycles). This work derives the counting series of the simple connected graphs that have cycles of unrestricted number and length, but no…
A linkage is a finite graph with lengths assigned to each edge. A planar realization is a map to the plane which preserves edge lengths. It can be thought of as a mechanical device formed from stiff rods and rotating joints. We look at the…
Linear quadratic graphon field games (LQ-GFGs) are defined to be LQ games which involve a large number of agents that are weakly coupled via a weighted undirected graph on which each node represents an agent. The links of the graph…
In this paper the Shapley value of digraph (directed graph) games are considered. Digraph games are transferable utility (TU) games with limited cooperation among players, where players are represented by nodes. A restrictive relation…
Taking the absolute value of consecutive differences of a cyclicly ordered list of integers constitutes a simple dynamical system. For lists of lenght a power of two the process will terminate in all zeros, but examples with arbitarily long…
Riddles are concise linguistic puzzles that describe an object or idea through indirect, figurative, or playful clues. They are a longstanding form of creative expression, requiring the solver to interpret hints, recognize patterns, and…