arXiv subjects

Samuel Wolf

Publications and source records attributed to Samuel Wolf.

4 recordsLinked to original sources

arXiv2026

Chunky Chains: Graph Drawings on Small Screens

We introduce Chunky Chains, a graph drawing style designed for small screens such as smartphones, where vertical scrolling is the dominant means of interaction. A Chunky Chain consists of a vertical chain of chord diagrams, called buckets. Vertices are placed as circular arcs on bucket boundaries, and edges are drawn inside a bucket or through gate nodes connecting consecutive buckets. Since every bucket contains only a bounded number of vertices, the drawing has bounded width. The combinatorial core is the choice of a bucket arrangement. Given a capacity $c$, the vertices are partitioned into an ordered set of buckets, each of size at most $c$. Edges whose endpoints lie in the same or in adjacent buckets are short. Edges that are "skipping" at least one bucket are long, and we draw them only partially. The goal is to minimize the number of long edges. We present a combinatorial framework for producing high quality Chunky Chains and analyze the complexity of its steps. We develop exact and heuristic algorithms, and experimentally evaluate their effectiveness. Our experiments show that many real-world graphs have good Chunky Chain visualizations. In a case study, we discuss Chunky Chains for graphs with certain temporal features.

cs.DS↗

arXiv2025

Planar Stories of Graph Drawings: Algorithms and Experiments

We address the problem of computing a dynamic visualization of a geometric graph $G$ as a sequence of frames. Each frame shows only a portion of the graph but their union covers $G$ entirely. The two main requirements of our dynamic visualization are: $(i)$ guaranteeing drawing stability, so to preserve the user's mental map; $(ii)$ keeping the visual complexity of each frame low. To satisfy the first requirement, we never change the position of the vertices. Regarding the second requirement, we avoid edge crossings in each frame. More precisely, in the first frame we visualize a suitable subset of non-crossing edges; in each subsequent frame, exactly one new edge enters the visualization and all the edges that cross with it are deleted. We call such a sequence of frames a planar story of $G$. Our goal is to find a planar story whose minimum number of edges contemporarily displayed is maximized (i.e., a planar story that maximizes the minimum frame size). Besides studying our model from a theoretical point of view, we also design and experimentally compare different algorithms, both exact techniques and heuristics. These algorithms provide an array of alternative trade-offs between efficiency and effectiveness, also depending on the structure of the input graph.

cs.CG↗

arXiv2025

Visualization of Event Graphs for Train Schedules

Train timetables can be represented as event graphs, where correspond to a train passing through a location at a certain point in time. A visual representation of an event graph is important for many applications such as dispatching and (the development of) dispatching software. A common way to represent event graphs are time-space diagrams. In such a diagram, key locations are visualized on the y-axis and time on the x-axis of a coordinate system. A train's movement is then represented as a connected sequence of line segments in this coordinate system. This visualization allows for an easy detection of infrastructure conflicts and safety distance violations. However, time-space diagrams are usually used only to depict event graphs that are restricted to corridors, where an obvious ordering of the locations exists. In this paper, we consider the visualization of general event graphs in time-space diagrams, where the challenge is to find an ordering of the locations that produces readable drawings. We argue that this means to minimize the number of turns, i.e., the total number of changes in y-direction. To this end, we establish a connection between this problem and Maximum Betweenness. Then we develop a preprocessing strategy to reduce the instance size. We also propose a parameterized algorithm and integer linear programming formulations. We experimentally evaluate the preprocessing strategy and the integer programming formulations on a real-world dataset. Our best algorithm solves every instance in the dataset in less than a second. This suggests that turn-optimal time-space diagrams can be computed in real time.

cs.CG↗

arXiv2025

Eliminating Majority Illusions

An opinion illusion refers to a phenomenon in social networks where agents may witness distributions of opinions among their neighbours that do not accurately reflect the true distribution of opinions in the population as a whole. A specific case of this occurs when there are only two possible choices, such as whether to receive the COVID-19 vaccine or vote on EU membership, which is commonly referred to as a majority illusion. In this work, we study the topological properties of social networks that lead to opinion illusions and focus on minimizing the number of agents that need to be influenced to eliminate these illusions. To do so, we propose an initial, but systematic study of the algorithmic behaviour of this problem. We show that the problem is NP-hard even for underlying topologies that are rather restrictive, being planar and of bounded diameter. We then look for exact algorithms that scale well as the input grows (FPT). We argue the in-existence of such algorithms even when the number of vertices that must be influenced is bounded, or when the social network is arranged in a ``path-like'' fashion (has bounded pathwidth). On the positive side, we present an FPT algorithm for networks with ``star-like'' structure (bounded vertex cover number). Finally, we construct an FPT algorithm for ``tree-like'' networks (bounded treewidth) when the number of vertices that must be influenced is bounded. This algorithm is then used to provide a PTAS for planar graphs.

cs.CC↗