7 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
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
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
Visualization Algorithms for Maps and Diagrams
One of the most common visualization tools used by mankind are maps or diagrams. In this thesis we explore new algorithms for visualizing maps (road and argument maps). A map without any textual information or pictograms is often without use so we
research also further into the field of labeling maps. In particular we consider the new challenges posed by interactive maps offered by mobile devices. We discuss new algorithmic approaches and experimentally evaluate them