Related papers: Measuring Board Game Distance

We identify the task of measuring data to quantitatively characterize the composition of machine learning data and datasets. Similar to an object's height, width, and volume, data measurements quantify different attributes of data along…

Lipman et al. [ACM Transactions on Graphics 29 (3) (2010), 1--11] introduced the concept of biharmonic distance to measure the distances between pairs of points on a 3D surface. Biharmonic distance has some advantages over resistance…

From the beginning if the history of AI, there has been interest in games as a platform of research. As the field developed, human-level competence in complex games became a target researchers worked to reach. Only relatively recently has…

With increasing interest in procedural content generation by academia and game developers alike, it is vital that different approaches can be compared fairly. However, evaluating procedurally generated video game levels is often difficult,…

In Model-Based Design of Cyber-Physical Systems (CPS), it is often desirable to develop several models of varying fidelity. Models of different fidelity levels can enable mathematical analysis of the model, control synthesis, faster…

-Much work has been devoted to the computational complexity of games. However, they are not necessarily relevant for estimating the complexity in human terms. Therefore, human-centered measures have been proposed, e.g. the depth. This paper…

High calorie intake in the human body on the one hand, has proved harmful in numerous occasions leading to several diseases and on the other hand, a standard amount of calorie intake has been deemed essential by dieticians to maintain the…

This letter employs differential game theory to address the defense problem of a circular target area with perception constraints, involving a single defender and a single attacker. The defender is restricted to moving along the perimeter,…

This paper considers a reach-avoid differential game in three-dimensional space with four equal-speed players. A plane divides the game space into a play subspace and a goal subspace. The evader aims at entering the goal subspace while…

We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…

This survey comprehensively reviews the multi-dimensionality of game scenario diversity, spotlighting the innovative use of procedural content generation and other fields as cornerstones for enriching player experiences through diverse game…

The cognitive framework of conceptual spaces [3] provides geometric means for representing knowledge. A conceptual space is a high-dimensional space whose dimensions are partitioned into so-called domains. Within each domain, the Euclidean…

This paper is about similarity between objects that can be represented as points in metric measure spaces. A metric measure space is a metric space that is also equipped with a measure. For example, a network with distances between its…

Distance games are games played on graphs in which the players alternately colour vertices, and which vertices can be coloured only depends on the distance to previously coloured vertices. The polynomial profile encodes the number of…

This work briefly explores the possibility of approximating spatial distance (alternatively, similarity) between data points using the Isolation Forest method envisioned for outlier detection. The logic is similar to that of isolation: the…

We provide several tests to determine whether a game is a potential game or whether it is a zero-sum equivalent game---a game which is strategically equivalent to a zero-sum game in the same way that a potential game is strategically…

This paper contributes a new way to evaluate AI. Much as one might evaluate a machine in terms of its performance at chess, this approach involves evaluating a machine in terms of its performance at a game called "MAD Chairs". At the time…

Increasing user engagement is constant challenge for Intelligent Tutoring Systems researchers. A current trend in the ITS field is to increase engagement of proven learning systems by integrating them within games, or adding in game like…

We present a definition of the distance between probability distributions. Our definition is based on the $L_1$ norm on space of probability measures. We compare our distance with the well-known Kullback-Leibler divergence and with the…

Distance measuring is a very important task in digital geometry and digital image processing. Due to our natural approach to geometry we think of the set of points that are equally far from a given point as a Euclidean circle. Using the…