13 research outputs found
SHARQL: Shape Analysis of Recursive SPARQL Queries
International audienceWe showcase SHARQL, a system that allows to navigate SPARQL query logs, can inspect complex queries by visualizing their shape, and can serve as a back-end to flexibly produce statistics about the logs. Even though SPARQL query logs are increasingly available and have become public recently, their navigation and analysis is hampered by the lack of appropriate tools. SPARQL queries are sometimes hard to understand and their inherent properties, such as their shape, their hypertree properties, and their property paths are even more difficult to be identified and properly rendered. In SHARQL, we show how the analysis and exploration of several hundred million queries is possible. We offer edge rendering which works with complex hyperedges, regular edges, and property paths of SPARQL queries. The underlying database stores more than one hundred attributes per query and is therefore extremely flexible for exploring the query logs and as a back-end to compute and display analytical properties of the entire logs or parts thereof
Simultaneous Embeddability of Two Partitions
We study the simultaneous embeddability of a pair of partitions of the same
underlying set into disjoint blocks. Each element of the set is mapped to a
point in the plane and each block of either of the two partitions is mapped to
a region that contains exactly those points that belong to the elements in the
block and that is bounded by a simple closed curve. We establish three main
classes of simultaneous embeddability (weak, strong, and full embeddability)
that differ by increasingly strict well-formedness conditions on how different
block regions are allowed to intersect. We show that these simultaneous
embeddability classes are closely related to different planarity concepts of
hypergraphs. For each embeddability class we give a full characterization. We
show that (i) every pair of partitions has a weak simultaneous embedding, (ii)
it is NP-complete to decide the existence of a strong simultaneous embedding,
and (iii) the existence of a full simultaneous embedding can be tested in
linear time.Comment: 17 pages, 7 figures, extended version of a paper to appear at GD 201
Constraint Generation Algorithm for the Minimum Connectivity Inference Problem
Given a hypergraph , the Minimum Connectivity Inference problem asks for a
graph on the same vertex set as with the minimum number of edges such that
the subgraph induced by every hyperedge of is connected. This problem has
received a lot of attention these recent years, both from a theoretical and
practical perspective, leading to several implemented approximation, greedy and
heuristic algorithms. Concerning exact algorithms, only Mixed Integer Linear
Programming (MILP) formulations have been experimented, all representing
connectivity constraints by the means of graph flows. In this work, we
investigate the efficiency of a constraint generation algorithm, where we
iteratively add cut constraints to a simple ILP until a feasible (and optimal)
solution is found. It turns out that our method is faster than the previous
best flow-based MILP algorithm on random generated instances, which suggests
that a constraint generation approach might be also useful for other
optimization problems dealing with connectivity constraints. At last, we
present the results of an enumeration algorithm for the problem.Comment: 16 pages, 4 tables, 1 figur
The role of twins in computing planar supports of hypergraphs
A support or realization of a hypergraph is a graph on the same
vertex as such that for each hyperedge of it holds that its vertices
induce a connected subgraph of . The NP-hard problem of finding a planar}
support has applications in hypergraph drawing and network design. Previous
algorithms for the problem assume that twins}---pairs of vertices that are in
precisely the same hyperedges---can safely be removed from the input
hypergraph. We prove that this assumption is generally wrong, yet that the
number of twins necessary for a hypergraph to have a planar support only
depends on its number of hyperedges. We give an explicit upper bound on the
number of twins necessary for a hypergraph with hyperedges to have an
-outerplanar support, which depends only on and . Since all
additional twins can be safely removed, we obtain a linear-time algorithm for
computing -outerplanar supports for hypergraphs with hyperedges if
and are constant; in other words, the problem is fixed-parameter
linear-time solvable with respect to the parameters and
Short Plane Supports for Spatial Hypergraphs
A graph is a support of a hypergraph if every hyperedge
induces a connected subgraph in . Supports are used for certain types of
hypergraph visualizations. In this paper we consider visualizing spatial
hypergraphs, where each vertex has a fixed location in the plane. This is the
case, e.g., when modeling set systems of geospatial locations as hypergraphs.
By applying established aesthetic quality criteria we are interested in finding
supports that yield plane straight-line drawings with minimum total edge length
on the input point set . We first show, from a theoretical point of view,
that the problem is NP-hard already under rather mild conditions as well as a
negative approximability results. Therefore, the main focus of the paper lies
on practical heuristic algorithms as well as an exact, ILP-based approach for
computing short plane supports. We report results from computational
experiments that investigate the effect of requiring planarity and acyclicity
on the resulting support length. Further, we evaluate the performance and
trade-offs between solution quality and speed of several heuristics relative to
each other and compared to optimal solutions.Comment: Appears in the Proceedings of the 26th International Symposium on
Graph Drawing and Network Visualization (GD 2018
MetroSets: Visualizing Sets as Metro Maps
We propose MetroSets, a new, flexible online tool for visualizing set systems
using the metro map metaphor. We model a given set system as a hypergraph
, consisting of a set of vertices and a set
, which contains subsets of called hyperedges. Our system then
computes a metro map representation of , where each hyperedge
in corresponds to a metro line and each vertex corresponds to a
metro station. Vertices that appear in two or more hyperedges are drawn as
interchanges in the metro map, connecting the different sets. MetroSets is
based on a modular 4-step pipeline which constructs and optimizes a path-based
hypergraph support, which is then drawn and schematized using metro map layout
algorithms. We propose and implement multiple algorithms for each step of the
MetroSet pipeline and provide a functional prototype with \new{easy-to-use
preset configurations.} % many real-world datasets. Furthermore, \new{using
several real-world datasets}, we perform an extensive quantitative evaluation
of the impact of different pipeline stages on desirable properties of the
generated maps, such as octolinearity, monotonicity, and edge uniformity.Comment: 19 pages; accepted for IEEE INFOVIS 2020; for associated live system,
see http://metrosets.ac.tuwien.ac.a