Results 1  10
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18
Three Rules Suffice for Good Label Placement
 Algorithmica Special Issue on GIS
, 2000
"... The general labelplacement problem consists in labeling a set of features (points, lines, regions) given a set of candidates (rectangles, circles, ellipses, irregularly shaped labels) for each feature. The problem arises when annotating classical cartographical maps, diagrams, or graph drawings. Th ..."
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Cited by 19 (2 self)
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The general labelplacement problem consists in labeling a set of features (points, lines, regions) given a set of candidates (rectangles, circles, ellipses, irregularly shaped labels) for each feature. The problem arises when annotating classical cartographical maps, diagrams, or graph drawings. The size of a labeling is the number of features that receive pairwise nonintersecting candidates. Finding an optimal solution, i.e. a labeling of maximum size, is NPhard. We present an approach to attack the problem in its full generality. The key idea is to separate the geometric part from the combinatorial part of the problem. The latter is captured by the conflict graph of the candidates. We present a set of rules that simplify the conflict graph without reducing the size of an optimal solution. Combining the application of these rules with a simple heuristic yields nearoptimal solutions. We study competing algorithms and do a thorough empirical comparison on pointlabeling data. The new algorithm we suggest is fast, simple, and effective.
Labeling Points with Weights
, 2001
"... . Annotating maps, graphs, and diagrams with pieces of text is an important step in information visualization that is usually referred to as label placement. We define nine labelplacement models for labeling points with axisparallel rectangles given a weight for each point. There are two group ..."
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Cited by 15 (3 self)
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. Annotating maps, graphs, and diagrams with pieces of text is an important step in information visualization that is usually referred to as label placement. We define nine labelplacement models for labeling points with axisparallel rectangles given a weight for each point. There are two groups; fixedposition models and slider models. We aim to maximize the weight sum of those points that receive a label. We first compare our models by giving bounds for the ratios between the weights of maximumweight labelings in di#erent models. Then we present algorithms for labeling n points with unitheight rectangles. We show how an O(n log n)time factor2 approximation algorithm and a PTAS for fixedposition models can be extended to handle the weighted case. Our main contribution is the first algorithm for weighted sliding labels. Its approximation factor is (2 + ε), it runs in O(n 2/ε) time and uses O(n²/#) space. We also investigate some special cases.
Optimal Labelling of Point Features in Rectangular Labelling Models
, 2000
"... We investigate the label number maximisation problem (lnm): Given a set of labels , each of which belongs to a point feature in the plane, the task is to find a largest subset P of so that each 2 P labels the corresponding point feature and no two labels from P overlap. Our approach is based ..."
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Cited by 13 (2 self)
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We investigate the label number maximisation problem (lnm): Given a set of labels , each of which belongs to a point feature in the plane, the task is to find a largest subset P of so that each 2 P labels the corresponding point feature and no two labels from P overlap. Our approach is based on two socalled constraint graphs which code horizontal and vertical positioning relations. The key idea is to link the two graphs by a set of additional constraints, thus characterising all feasible solutions of lnm. This enables us to formulate a zeroone integer linear program whose solution leads to an optimal labelling. We can express lnm in both the discrete and the slider labelling models. The slider models allow a continuous movement of a label around its point feature, leading to a significantly higher number of labels that can be placed. To our knowledge, we present the first algorithm that computes provably optimal solutions in the slider models. We find it remarkable that our approach is independent of the labelling model and results in a discrete algorithm even if the problem is of continuous nature as in the slider models. Extensive experimental results on both realworld instances and point sets created by a widely used benchmark generator show that the new approach is applicable in practice.
ForceBased Label Number Maximation
, 2003
"... We present a forcebased simulated annealing algorithm to heuristically solve the NPhard label number maximization problem LNM: Given a set of rectangular labels, each of which belongs to a pointfeature in the plane, the task is to find a labeling for a largest subset of the labels. A labeling ..."
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Cited by 10 (0 self)
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We present a forcebased simulated annealing algorithm to heuristically solve the NPhard label number maximization problem LNM: Given a set of rectangular labels, each of which belongs to a pointfeature in the plane, the task is to find a labeling for a largest subset of the labels. A labeling is a placement such that none of the labels overlap and each is placed at its pointfeature. The
Optimal Algorithm for a Special Pointlabeling Problem
 INFORMATION PROCESSING LETTERS
, 2002
"... We investigate a special class of map labeling problem. Let P = fp1 ; p2 ; : : : ; png be a set of point sites distributed on a 2D map. A label associated with each point is a axisparallel rectangle of a constant height but of variable width. Here height of a label indicates the font size and w ..."
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Cited by 6 (1 self)
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We investigate a special class of map labeling problem. Let P = fp1 ; p2 ; : : : ; png be a set of point sites distributed on a 2D map. A label associated with each point is a axisparallel rectangle of a constant height but of variable width. Here height of a label indicates the font size and width indicates the number of characters in that label. For a point p i , its label contains the point p i at its topleft or bottomleft corner, and it does not obscure any other point in P . Width of the label for each point in P is known in advance. The objective is to label the maximum number of points on the map so that the placed labels are mutually nonoverlapping. We first consider
Label updating to avoid pointshaped obstacles in fixed model
, 2006
"... In this paper, we present efficient algorithms for updating the labeling of a set of n points after the presence of a random obstacle that appears on the map repeatedly. We update the labeling so that the given obstacle does not appear in any of the labels, the new labeling is valid, and the labels ..."
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Cited by 2 (2 self)
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In this paper, we present efficient algorithms for updating the labeling of a set of n points after the presence of a random obstacle that appears on the map repeatedly. We update the labeling so that the given obstacle does not appear in any of the labels, the new labeling is valid, and the labels are as large as possible (called the optimal labeling). Each point is assumed to have an axisparallel, squareshaped label of unit size, attached exclusively to that point in the middle of one of its edges. We consider two models: (1) the 2PM model, where each label is attached to its feature only on the middle of one of its horizontal edges, and (2) the r4PM model, where each label is attached to its feature on the middle of either one of its horizontal or vertical edges (known in advance). We assume that a sequence of pointshaped obstacles appear on the map on random locations. Three settings are considered for the behavior of the obstacle: (1) the obstacle is removed afterwards, (2) it remains on the map, and (3) it receives a similar label and remains on the map. Only two operations are permitted on the labels: flipping one or more labels, and/or resizing all labels. In the first setting, we suggest a data structure of O(n) space and O(n lg n) time in the 2PM model, and of O(n 2) time in the r4PM model, so that the updated labeling can be constructed for any obstacle position in O(lg n + k) time, where k is the minimum number of operations needed. For the second and third problems, we suggest an O(n) space and O(n lg n) time data structure that can place each obstacle (possibly with a label) on the map in O(lg n + k) time, if k label flips are sufficient to make room to place the new
A case study of combined text and icon placement
, 2005
"... This paper examines a method of combining text label and icon placement in maps created in realtime. The method is divided into four steps. In the first step candidate positions of the text labels are chosen, and in the second step candidate positions of the icons. The choice of candidate positions ..."
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Cited by 1 (0 self)
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This paper examines a method of combining text label and icon placement in maps created in realtime. The method is divided into four steps. In the first step candidate positions of the text labels are chosen, and in the second step candidate positions of the icons. The choice of candidate positions do not consider overlaps between labels and icons. The overlaps are resolved in the third step, which is based on a combinatorial optimization technique (simulated annealing). In the fourth and final step labels that overlap can be removed. The main theme of this paper is a study for defining the candidate positions before the combinatorial optimization. A case study is performed where the number of candidate positions varies as well as the selection strategy (random or stratified). The case study indicates that, for our test set up, a large number of randomly selected candidate positions give the worst result.
Unit height kposition map labeling
 in Proc.19th European Workshop on Computational Geometry (EWCG'03
, 2003
"... ..."
Sliding labels for dynamic point labeling
"... We study a dynamic labeling problem for points on a line that is closely related to labeling of zoomable maps. Typically, labels have a constant size on screen, which means that, as the scale of the map decreases during zooming, the labels grow relatively to the set of points, and conflicts may occu ..."
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Cited by 1 (0 self)
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We study a dynamic labeling problem for points on a line that is closely related to labeling of zoomable maps. Typically, labels have a constant size on screen, which means that, as the scale of the map decreases during zooming, the labels grow relatively to the set of points, and conflicts may occur due to overlapping labels. Our algorithmic problem is a combined dynamic selection and placement problem in a slidinglabel model: (i) select for each label ℓ a contiguous active range of map scales at which ℓ is displayed, and (ii) place each label at an appropriate position relative to its anchor point by sliding it along the point. The active range optimization (ARO) problem is to select active ranges and slider positions so that no two labels intersect at any scale and the sum of the lengths of active ranges is maximized. We present a dynamic programming algorithm to solve the discrete kposition ARO problem optimally and an FPTAS for the continuous sliding ARO problem. 1
RealTime Map Labeling for Personal Navigation
 Atlantic, University of Gävle
, 2004
"... This paper aims to examine realtime map labelling methods for personal navigation using smalldisplay mobile devices such as PDAs. It’s essential to label roads, landmarks, and other important features on navigational maps, which will help users to understand their location and the environment. Thi ..."
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Cited by 1 (0 self)
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This paper aims to examine realtime map labelling methods for personal navigation using smalldisplay mobile devices such as PDAs. It’s essential to label roads, landmarks, and other important features on navigational maps, which will help users to understand their location and the environment. This paper proposes a method to label both line and point features using a slider model, which makes it possible to choose label positions from infinite search space. We implemented this method in a Java environment. A case study shows sound cartographic results of the labelling.