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44
An Empirical Study of Algorithms for Point Feature Label Placement
, 1994
"... A major factor affecting the clarity of graphical displays that include text labels is the degree to which labels obscure display features (including other labels) as a result of spatial overlap. Pointfeature label placement (PFLP) is the problem of placing text labels adjacent to point features on ..."
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Cited by 160 (8 self)
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A major factor affecting the clarity of graphical displays that include text labels is the degree to which labels obscure display features (including other labels) as a result of spatial overlap. Pointfeature label placement (PFLP) is the problem of placing text labels adjacent to point features on a map or diagram so as to maximize legibility. This problem occurs frequently in the production of many types of informational graphics, though it arises most often in automated cartography. In this paper we present a comprehensive treatment of the PFLP problem, viewed as a type of combinatorial optimization problem. Complexity analysis reveals that the basic PFLP problem and most interesting variants of it are NPhard. These negative results help inform a survey of previously reported algorithms for PFLP; not surprisingly, all such algorithms either have exponential time complexity or are incomplete. To solve the PFLP problem in practice, then, we must rely on good heuristic methods. We pr...
A General Cartographic Labeling Algorithm
, 1996
"... Some apparently powerful algorithms for automatic label placement on maps use heuristics that capture considerable cartographic expertise but are hampered by provably inefficient methods of search and optimization. On the other hand, no approach to label placement that is based on an efficient optim ..."
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Cited by 49 (2 self)
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Some apparently powerful algorithms for automatic label placement on maps use heuristics that capture considerable cartographic expertise but are hampered by provably inefficient methods of search and optimization. On the other hand, no approach to label placement that is based on an efficient optimization technique has been applied to the production of general cartographic maps  those with labeled point, line, and area features  and shown to generate labelings of acceptable quality. We present an algorithm for label placement that achieves the twin goals of practical efficiency and high labeling quality by combining simple cartographic heuristics with effective stochastic optimization techniques. To appear in Cartographica. 1 Introduction Many apparently compelling techniques for automatic label placement use sophisticated heuristics for capturing cartographic knowledge, but, as noted by Zoraster (1991), also use inferior optimization strategies for finding good tradeoffs betwe...
Boundary labeling: Models and efficient algorithms for rectangular maps
, 2004
"... In this paper, we present boundary labeling, a new approach for labeling point sets with large labels. We first place disjoint labels around an axisparallel rectangle that contains the points. Then we connect each label to its point such that no two connections intersect. Such an approach is commo ..."
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Cited by 36 (11 self)
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In this paper, we present boundary labeling, a new approach for labeling point sets with large labels. We first place disjoint labels around an axisparallel rectangle that contains the points. Then we connect each label to its point such that no two connections intersect. Such an approach is common e.g. in technical drawings and medical atlases, but so far the problem has not been studied in the literature. The new problem is interesting in that it is a mixture of a labelplacement and a graphdrawing problem.
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.
Tabu search heuristic for pointfeature cartographic label placement
 GeoInformatica and International Journal on Advances of Computer Science for Geographic Information Systems
, 2002
"... Abstract. The generation of better label placement configurations in maps is a problem that comes up in automated cartographic production. The objective of a good label placement is to display the geographic position of the features with their corresponding label in a clear and harmonious fashion, f ..."
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Cited by 19 (2 self)
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Abstract. The generation of better label placement configurations in maps is a problem that comes up in automated cartographic production. The objective of a good label placement is to display the geographic position of the features with their corresponding label in a clear and harmonious fashion, following accepted cartographic conventions. In this work, we have approached this problem from a combinatorial optimization point of view, and our research consisted of the evaluation of the Tabu Search (TS) heuristic applied to cartographic label placement. When compared, in real and random test cases, with techniques such as simulated annealing and genetic algorithm (GA), TS has proven to be an efficient choice, with the best performance in quality. We concluded that TS is a recommended method to solve cartographic label placement problem of point features, due to its simplicity, practicality, efficiency and good performance along with its ability to generate quality solutions in acceptable computational time.
Algorithms for Maximum Independent Set Applied to Map Labelling
, 2000
"... We consider the following map labelling problem: given distinct points p 1 , p 2 , . . . , p n in the plane, and given #, find a maximum cardinality set of pairwise disjoint axisparallel # # squares Q 1 , Q 2 , . . . , Q r . This problem reduces to that of finding a maximum cardinality indepe ..."
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Cited by 18 (0 self)
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We consider the following map labelling problem: given distinct points p 1 , p 2 , . . . , p n in the plane, and given #, find a maximum cardinality set of pairwise disjoint axisparallel # # squares Q 1 , Q 2 , . . . , Q r . This problem reduces to that of finding a maximum cardinality independent set in an associated graph called the conflict graph. We describe several heuristics for the maximum cardinality independent set problem, some of which use an LP solution as input. Also, we describe a branchandcut algorithm to solve it to optimality. The standard independent set formulation has an inequality for each edge in the conflict graph which ensures that only one of its endpoints can belong to an independent set. To obtain good starting points for our LPbased heuristics and good upper bounds on the optimal value for our branchandcut algorithm we replace this set of inequalities by the set of inequalities describing all maximal cliques in the conflict graph. For this streng...
The Metro Map Layout Problem
"... Abstract. We initiate a new problem of automatic metro map layout. In general, a metro map consists of a set of lines which have intersections or overlaps. We define a set of aesthetic criteria for good metro map layouts and present a method to produce such layouts automatically. Our method uses a v ..."
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Cited by 18 (4 self)
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Abstract. We initiate a new problem of automatic metro map layout. In general, a metro map consists of a set of lines which have intersections or overlaps. We define a set of aesthetic criteria for good metro map layouts and present a method to produce such layouts automatically. Our method uses a variation of the spring algorithm with a suitable preprocessing step. The experimental results with real world data sets show that our method produces good metro map layouts quickly. 1
On the Edge Label Placement Problem
 Graph Drawing (Proc. GD '96
, 1997
"... . Let G(V;E) be a graph, and let f : G ! R 2 be a one to one function that produces a layout of a graph G on the plane. We consider the problem of assigning text labels to every edge of the graph such that the quality of the labeling assignment is optimal. This problem has been first encountered ..."
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Cited by 18 (3 self)
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. Let G(V;E) be a graph, and let f : G ! R 2 be a one to one function that produces a layout of a graph G on the plane. We consider the problem of assigning text labels to every edge of the graph such that the quality of the labeling assignment is optimal. This problem has been first encountered in automated cartography and has been referred to as the Line Feature Label Placement (LFLP) problem. Even though much effort has been devoted over the last 15 years in the area of automated drawing of maps, the Edge Label Placement (ELP) problem has received little attention. In this paper we investigate computational complexity issues of the ELP problem, which have been open up to the present time. Specifically we prove that the ELP problem is NPHard. 1 Introduction In recent years graph drawing has received increasing attention due to the large number of applications, such as, entity relationship diagrams, software engineering diagrams, CASE tools, debugging tools, communication network...
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.