8 research outputs found
Trajectory-Based Dynamic Map Labeling
In this paper we introduce trajectory-based labeling, a new variant of
dynamic map labeling, where a movement trajectory for the map viewport is
given. We define a general labeling model and study the active range
maximization problem in this model. The problem is NP-complete and W[1]-hard.
In the restricted, yet practically relevant case that no more than k labels can
be active at any time, we give polynomial-time algorithms. For the general case
we present a practical ILP formulation with an experimental evaluation as well
as approximation algorithms.Comment: 19 pages, 7 figures, extended version of a paper to appear at ISAAC
201
Evaluation of Labeling Strategies for Rotating Maps
We consider the following problem of labeling points in a dynamic map that
allows rotation. We are given a set of points in the plane labeled by a set of
mutually disjoint labels, where each label is an axis-aligned rectangle
attached with one corner to its respective point. We require that each label
remains horizontally aligned during the map rotation and our goal is to find a
set of mutually non-overlapping active labels for every rotation angle so that the number of active labels over a full map rotation of
2 is maximized. We discuss and experimentally evaluate several labeling
models that define additional consistency constraints on label activities in
order to reduce flickering effects during monotone map rotation. We introduce
three heuristic algorithms and compare them experimentally to an existing
approximation algorithm and exact solutions obtained from an integer linear
program. Our results show that on the one hand low flickering can be achieved
at the expense of only a small reduction in the objective value, and that on
the other hand the proposed heuristics achieve a high labeling quality
significantly faster than the other methods.Comment: 16 pages, extended version of a SEA 2014 pape
Consistent labeling of rotating maps
Dynamic maps that allow continuous map rotations, for example, on mobile
devices, encounter new geometric labeling issues unseen in static maps before. We study the
following dynamic map labeling problem: The input is an abstract map consisting of a set P
of points in the plane with attached horizontally aligned rectangular labels. While the map
with the point set P is rotated, all labels remain horizontally aligned. We are interested in
a consistent labeling of P under rotation, i.e., an assignment of a single (possibly empty)
active interval of angles for each label that determines its visibility under rotations such
that visible labels neither intersect each other (soft conflicts) nor occlude points in P at any
rotation angle (hard conflicts). Our goal is to find a consistent labeling that maximizes the
number of visible labels integrated over all rotation angles.
We first introduce a general model for labeling rotating maps and derive basic geometric
properties of consistent solutions. We show NP-hardness of the above optimization
problem even for unit-square labels. We then present a constant-factor approximation for
this problem based on line stabbing, and refine it further into an efficient polynomial-time
approximation scheme (EPTAS)
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