19 research outputs found
Many-to-One Boundary Labeling with Backbones
In this paper we study \emph{many-to-one boundary labeling with backbone
leaders}. In this new many-to-one model, a horizontal backbone reaches out of
each label into the feature-enclosing rectangle. Feature points that need to be
connected to this label are linked via vertical line segments to the backbone.
We present dynamic programming algorithms for label number and total leader
length minimization of crossing-free backbone labelings. When crossings are
allowed, we aim to obtain solutions with the minimum number of crossings. This
can be achieved efficiently in the case of fixed label order, however, in the
case of flexible label order we show that minimizing the number of leader
crossings is NP-hard.Comment: 23 pages, 10 figures, this is the full version of a paper that is
about to appear in GD'1
Planar Drawings of Fixed-Mobile Bigraphs
A fixed-mobile bigraph G is a bipartite graph such that the vertices of one
partition set are given with fixed positions in the plane and the mobile
vertices of the other part, together with the edges, must be added to the
drawing. We assume that G is planar and study the problem of finding, for a
given k >= 0, a planar poly-line drawing of G with at most k bends per edge. In
the most general case, we show NP-hardness. For k=0 and under additional
constraints on the positions of the fixed or mobile vertices, we either prove
that the problem is polynomial-time solvable or prove that it belongs to NP.
Finally, we present a polynomial-time testing algorithm for a certain type of
"layered" 1-bend drawings
Multi-Sided Boundary Labeling
In the Boundary Labeling problem, we are given a set of points, referred
to as sites, inside an axis-parallel rectangle , and a set of pairwise
disjoint rectangular labels that are attached to from the outside. The task
is to connect the sites to the labels by non-intersecting rectilinear paths,
so-called leaders, with at most one bend.
In this paper, we study the Multi-Sided Boundary Labeling problem, with
labels lying on at least two sides of the enclosing rectangle. We present a
polynomial-time algorithm that computes a crossing-free leader layout if one
exists. So far, such an algorithm has only been known for the cases in which
labels lie on one side or on two opposite sides of (here a crossing-free
solution always exists). The case where labels may lie on adjacent sides is
more difficult. We present efficient algorithms for testing the existence of a
crossing-free leader layout that labels all sites and also for maximizing the
number of labeled sites in a crossing-free leader layout. For two-sided
boundary labeling with adjacent sides, we further show how to minimize the
total leader length in a crossing-free layout
On Embeddability of Buses in Point Sets
Set membership of points in the plane can be visualized by connecting
corresponding points via graphical features, like paths, trees, polygons,
ellipses. In this paper we study the \emph{bus embeddability problem} (BEP):
given a set of colored points we ask whether there exists a planar realization
with one horizontal straight-line segment per color, called bus, such that all
points with the same color are connected with vertical line segments to their
bus. We present an ILP and an FPT algorithm for the general problem. For
restricted versions of this problem, such as when the relative order of buses
is predefined, or when a bus must be placed above all its points, we provide
efficient algorithms. We show that another restricted version of the problem
can be solved using 2-stack pushall sorting. On the negative side we prove the
NP-completeness of a special case of BEP.Comment: 19 pages, 9 figures, conference version at GD 201
Visualizing Geophylogenies - Internal and External Labeling with Phylogenetic Tree Constraints
A geophylogeny is a phylogenetic tree where each leaf (biological taxon) has an associated geographic location (site). To clearly visualize a geophylogeny, the tree is typically represented as a crossing-free drawing next to a map. The correspondence between the taxa and the sites is either shown with matching labels on the map (internal labeling) or with leaders that connect each site to the corresponding leaf of the tree (external labeling). In both cases, a good order of the leaves is paramount for understanding the association between sites and taxa. We define several quality measures for internal labeling and give an efficient algorithm for optimizing them. In contrast, minimizing the number of leader crossings in an external labeling is NP-hard. We show nonetheless that optimal solutions can be found in a matter of seconds on realistic instances using integer linear programming. Finally, we provide several efficient heuristic algorithms and experimentally show them to be near optimal on real-world and synthetic instances
LIPIcs, Volume 277, GIScience 2023, Complete Volume
LIPIcs, Volume 277, GIScience 2023, Complete Volum