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Euler diagrams are a tool for the graphical representation of set relations. Due to their simple way of visualizing elements in the sets by geometric containment, they are easily readable by an inexperienced reader. Euler diagrams where the…
Markov decision processes capture sequential decision making under uncertainty, where an agent must choose actions so as to optimize long term reward. The paper studies efficient reasoning mechanisms for Relational Markov Decision Processes…
Resource allocation and scheduling are a common problem in various distributed systems. Although widely studied, the state-of-the-art solutions either do not scale or lack the expressive power to capture the most complex instances of the…
Order diagrams are an important tool to visualize the complex structure of ordered sets. Favorable drawings of order diagrams, i.e., easily readable for humans, are hard to come by, even for small ordered sets. Many attempts were made to…
Ranking over sets arise when users choose between groups of items. For example, a group may be of those movies deemed $5$ stars to them, or a customized tour package. It turns out, to model this data type properly, we need to investigate…
The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation…
Wiring diagrams, as seen in digital circuits, can be nested hierarchically and thus have an aspect of self-similarity. We show that wiring diagrams form the morphisms of an operad $\mcT$, capturing this self-similarity. We discuss the…
We consider a bandit problem over a graph where the rewards are not directly observed. Instead, the decision maker can compare two nodes and receive (stochastic) information pertaining to the difference in their value. The graph structure…
Bipartite graphs model the relationship between two disjoint sets of objects. They have a wide range of applications and are often visualized as a 2-layered drawing, where each set of objects is visualized as a set of vertices (points) on…
We investigate the win-lose relations between strategies of iterated prisoner's dilemma games by using a directed network concept to display the replicator dynamics results. In the giant strongly-connected component of the win/lose network,…
Complex systems, such as economic, social, biological, and ecological systems, usually feature interactions not only between pairwise entities but also among three or more entities. These multi-entity interactions are known as higher-order…
Here we introduce a model in which individuals differ in the rate at which they seek new interactions with others, making rational decisions modeled as general symmetric two-player games. Once a link between two individuals has formed, the…
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.…
Ranking athletes by their performance in competitions and tournaments is common in every popular sport and has significant benefits that contribute to both the organization and strategic aspects of competitions. Although rankings are…
We present an application of mosaic diagrams to the visualisation of set relations. Venn and Euler diagrams are the best known visual representations of sets and their relationships (intersections, containment or subsets, exclusion or…
A vertex ranking of a graph is an assignment of ranks (or colors) to the vertices of the graph, in such a way that any simple path connecting two vertices of equal rank, must contain a vertex of a higher rank. In this paper we study a…
Recently bipartite graphs have been widely used to represent the relationship two sets of items for information retrieval applications. The Web offers a wide range of data which can be represented by bipartite graphs, such us movies and…
Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…
Linear diagrams are an effective way to visualize set-based data by representing elements as columns and sets as rows with one or more horizontal line segments, whose vertical overlaps with other rows indicate set intersections and their…
Data visualizations present a massive number of potential messages to an observer. One might notice that one group's average is larger than another's, or that a difference in values is smaller than a difference between two others, or any of…