Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1709.01055

Computing Storyline Visualizations with Few Block Crossings

Thomas C. van Dijk·Fabian Lipp·Peter Markfelder·Alexander Wolff
View original source ↗Read source document ↗Export metadata ↓

Abstract

Storyline visualizations show the structure of a story, by depicting the interactions of the characters over time. Each character is represented by an x-monotone curve from left to right, and a meeting is represented by having the curves of the participating characters run close together for some time. There have been various approaches to drawing storyline visualizations in an automated way. In order to keep the visual complexity low, rather than minimizing pairwise crossings of curves, we count block crossings, that is, pairs of intersecting bundles of lines. Partly inspired by the ILP-based approach of Gronemann et al. [GD 2016] for minimizing the number of pairwise crossings, we model the problem as a satisfiability problem (since the straightforward ILP formulation becomes more complicated and harder to solve). Having restricted ourselves to a decision problem, we can apply powerful SAT solvers to find optimal drawings in reasonable time. We compare this SAT-based approach with two exact algorithms for block crossing minimization, using both the benchmark instances of Gronemann et al. and random instances. We show that the SAT approach is suitable for real-world instances and identify cases where the other algorithms are preferable.

Explore related subjects

cs.CGcs.DM

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Thomas C. van Dijk, Fabian Lipp, Peter Markfelder, Alexander Wolff. 2017-09-04. Computing Storyline Visualizations with Few Block Crossings. https://arxiv.org/abs/1709.01055

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Almost Linear Universal Point Sets for Planar Graphs

A point set is universal for planar graphs on $n$ vertices if every such graph has a straight-line drawing without crossings whose vertices belong to the set. We construct universal point sets of size $n^{1+o(1)}$, improving the previous quadratic upper bound. Our construction uses the reduction of Bannister, Cheng, Devanny, and Eppstein from universal point sets to superpatterns for $213$-avoiding permutations. We represent these permutations by ordered rooted forests and construct a small family of intervals containing every such forest. The result follows from a straightforward bound on the size of the family of intervals. GPT-6 Astra assisted in developing the construction and proof.

cs.CG↗
arXiv2026

Some results on Archdeacon's conjecture for rotation systems

A rotation system on $n$ elements assigns to each element a cyclic order of the other $n-1$ elements. A four-element subset is non-planar if its induced rotation system cannot be realized by a crossing-free drawing of $K_4$. As a combinatorial strengthening of Hill's conjecture on the crossing number of the complete graph, Archdeacon conjectured that every rotation system on $n$ elements has at least $H(n)=\frac{1}{4} \lfloor\frac {n}{2}\rfloor \lfloor\frac{n-1}{2}\rfloor \lfloor\frac{n-2}{2}\rfloor \lfloor\frac{n-3}{2}\rfloor$ non-planar four-element subsets. We computationally verify Archdeacon's conjecture for $n\leq 10$ and show that every extremal rotation system in these orders is realizable by a simple drawing. With computer assistance, we prove that every rotation system on $n$ elements has at least $(8/9 - o(1)) H(n)$ non-planar four-element subsets. We also present a proof by hand for a weaker lower bound of $(2/3-o(1)) H(n)$. Finally, extending recent work of Felsner on antipodal pairs in drawings, we show that Archdeacon's conjecture holds for antipodally shellable rotation systems.

cs.CG↗
arXiv2026

The Hyperbolic Surface Distance, Diameter, and Dirichlet Problems

Despite the prominence of hyperbolic surfaces in mathematics, basic algorithmic questions about them, even computing the distance between two points, have remained open, leaving many features of these surfaces inaccessible. The classical machinery assumes a polyhedral structure absent on a smooth surface. We remove these obstacles. We begin with an efficient $O(g^2)$ algorithm for the distance between two points, where $g$ is the genus of the surface. Building on it, we obtain an $O(g^2 \log g)$ method for answering distance queries from a fixed source and, as a consequence, for recentering a Dirichlet domain around an arbitrary point. This understanding of distances on the surface then lets us approximate the diameter to within any $\eps$ in time $O(g^3 \log g / \eps^2)$. We further show that the diameter, a single real number encoding a great deal about the surface, is exactly computable. Its hyperbolic cosine is an algebraic number over the field encoding the coefficients of the hyperbolic isometries defining the surface.

cs.CG↗