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Jules Wulms

Publications and source records attributed to Jules Wulms.

24 records · Page 2Linked to original sources
arXiv2021

Layered Area-Proportional Rectangle Contact Representations

We investigate two optimization problems on area-proportional rectangle contact representations for layered, embedded planar graphs. The vertices are represented as interior-disjoint unit-height rectangles of prescribed widths, grouped in one row per layer, and each edge is ideally realized as a rectangle contact of positive length. Such rectangle contact representations find applications in semantic word or tag cloud visualizations, where a collection of words is displayed such that pairs of semantically related words are close to each other. In this paper, we want to maximize the number of realized rectangle contacts or minimize the overall area of the rectangle contact representation, while avoiding any false adjacencies. We present a network flow model for area minimization, a linear-time algorithm for contact maximization of two-layer graphs, and an ILP model for maximizing contacts of $k$-layer graphs.

cs.CG↗
arXiv2021

Topological Stability of Kinetic $k$-Centers

We study the $k$-center problem in a kinetic setting: given a set of continuously moving points $P$ in the plane, determine a set of $k$ (moving) disks that cover $P$ at every time step, such that the disks are as small as possible at any point in time. Whereas the optimal solution over time may exhibit discontinuous changes, many practical applications require the solution to be stable: the disks must move smoothly over time. Existing results on this problem require the disks to move with a bounded speed, but this model allows positive results only for $k<3$. Hence, the results are limited and offer little theoretical insight. Instead, we study the topological stability of $k$-centers. Topological stability was recently introduced and simply requires the solution to change continuously, but may do so arbitrarily fast. We prove upper and lower bounds on the ratio between the radii of an optimal but unstable solution and the radii of a topologically stable solution -- the topological stability ratio -- considering various metrics and various optimization criteria. For $k = 2$ we provide tight bounds, and for small $k > 2$ we can obtain nontrivial lower and upper bounds. Finally, we provide an algorithm to compute the topological stability ratio in polynomial time for constant $k$.

cs.CG↗
arXiv2021

Stable Visual Summaries for Trajectory Collections

The availability of devices that track moving objects has led to an explosive growth in trajectory data. When exploring the resulting large trajectory collections, visual summaries are a useful tool to identify time intervals of interest. A typical approach is to represent the spatial positions of the tracked objects at each time step via a one-dimensional ordering; visualizations of such orderings can then be placed in temporal order along a time line. There are two main criteria to assess the quality of the resulting visual summary: spatial quality -- how well does the ordering capture the structure of the data at each time step, and stability -- how coherent are the orderings over consecutive time steps or temporal ranges? In this paper we introduce a new Stable Principal Component (SPC) method to compute such orderings, which is explicitly parameterized for stability, allowing a trade-off between the spatial quality and stability. We conduct extensive computational experiments that quantitatively compare the orderings produced by ours and other stable dimensionality-reduction methods to various state-of-the-art approaches using a set of well-established quality metrics that capture spatial quality and stability. We conclude that stable dimensionality reduction outperforms existing methods on stability, without sacrificing spatial quality or efficiency; in particular, our new SPC method does so at a fraction of the computational costs.

cs.HC↗
arXiv2019

Stability analysis of kinetic orientation-based shape descriptors

We study three orientation-based shape descriptors on a set of continuously moving points: the first principal component, the smallest oriented bounding box and the thinnest strip. Each of these shape descriptors essentially defines a cost capturing the quality of the descriptor and uses the orientation that minimizes the cost. This optimal orientation may be very unstable as the points are moving, which is undesirable in many practical scenarios. If we bound the speed with which the orientation of the descriptor may change, this may lower the quality of the resulting shape descriptor. In this paper we study the trade-off between stability and quality of these shape descriptors. We first show that there is no stateless algorithm, an algorithm that keeps no state over time, that both approximates the minimum cost of a shape descriptor and achieves continuous motion for the shape descriptor. On the other hand, if we can use the previous state of the shape descriptor to compute the new state, we can define "chasing" algorithms that attempt to follow the optimal orientation with bounded speed. We show that, under mild conditions, chasing algorithms with sufficient bounded speed approximate the optimal cost at all times for oriented bounding boxes and strips. The analysis of such chasing algorithms is challenging and has received little attention in literature, hence we believe that our methods used in this analysis are of independent interest.

cs.CG↗
arXiv2017

The Painter's Problem: covering a grid with colored connected polygons

Motivated by a new way of visualizing hypergraphs, we study the following problem. Consider a rectangular grid and a set of colors $χ$. Each cell $s$ in the grid is assigned a subset of colors $χ_s \subseteq χ$ and should be partitioned such that for each color $c\in χ_s$ at least one piece in the cell is identified with $c$. Cells assigned the empty color set remain white. We focus on the case where $χ= \{\text{red},\text{blue}\}$. Is it possible to partition each cell in the grid such that the unions of the resulting red and blue pieces form two connected polygons? We analyze the combinatorial properties and derive a necessary and sufficient condition for such a painting. We show that if a painting exists, there exists a painting with bounded complexity per cell. This painting has at most five colored pieces per cell if the grid contains white cells, and at most two colored pieces per cell if it does not.

cs.CG↗
arXiv2015

Continuous integration in a social-coding world: Empirical evidence from GitHub. **Updated version with corrections**

Continuous integration is a software engineering practice of frequently merging all developer working copies with a shared main branch, e.g., several times a day. With the advent of GitHub, a platform well known for its "social coding" features that aid collaboration and sharing, and currently the largest code host in the open source world, collaborative software development has never been more prominent. In GitHub development one can distinguish between two types of developer contributions to a project: direct ones, coming from a typically small group of developers with write access to the main project repository, and indirect ones, coming from developers who fork the main repository, update their copies locally, and submit pull requests for review and merger. In this paper we explore how GitHub developers use continuous integration as well as whether the contribution type (direct versus indirect) and different project characteristics (e.g., main programming language, or project age) are associated with the success of the automatic builds.

cs.SE↗