Elastic Labels Around the Perimeter of a Map

Iturriaga, Claudia; Lubiw, Anna

doi:10.1007/3-540-48447-7_31

Cited by 10 publications

(9 citation statements)

References 7 publications

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“…In the "Elastic labeling" model, each point receives a rectangular label where its area is fixed globally, and the goal is to find the maximum value of area size [7] where all points can be labeled. In this problem, if all points are positioned on the positive part of x and y axis and labels are placed in the first quarter of Euclidean 2D-space, then the optimal labeling can be found in polynomial time using a dynamic programming algorithm [8,6].…”

Section: Introductionmentioning

confidence: 99%

Incremental labeling in closed-2PM model

Rostamabadi

Ghodsi

2010

Computers & Electrical Engineering

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We consider an incremental optimal label placement in a closed-2PM map containing points each attached with a label. Labels are assumed to be axis-parallel square-shaped and have to be pairwise disjoint with maximum possible length each attached to its corresponding point on one of its horizontal edges. Such a labeling is denoted as optimal labeling. Our goal is to efficiently generate a new optimal labeling for all points after each new point being inserted in the map. Inserting each point may require several labels to flip or all labels to shrink. We present an algorithm that generates each new optimal labeling in O(lg n + k) time where k is the number of required label flips, if there is no need to shrink the label lengths, or in O(n) time when we have to shrink the labels and flip some of them. The algorithm uses O(n) space in both cases. This is a new result on this problem.

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Section: Introductionmentioning

confidence: 99%

Incremental labeling in closed-2PM model

Rostamabadi

Ghodsi

2010

Computers & Electrical Engineering

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“…Iturriaga and Lubiw [10] give an O(n 4 )-time decision algorithm for attaching elastic labels to n points on the perimeter of a rectangle. An elastic label models a block of text of fixed area, but varying width and height.…”

Section: Introductionmentioning

confidence: 99%

Boundary Labeling: Models and Efficient Algorithms for Rectangular Maps

et al. 2005

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Abstract. In this paper, we present boundary labeling, a new approach for labeling point sets with large labels. We first place disjoint labels around an axis-parallel 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 label-placement and a graph-drawing problem.

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“…How to place labels so that they do not overlap, is a well-known important problem in cartography. Thus, there are many research results on this topic and many algorithms have been developed for labeling points that are on lines [7,8,9,15] or in a region [5,6,10,11,12,14,17,19]. In the ACM Computational Geometry Impact Task Force report [2] the map label placement is listed as an important research area.…”

Section: Introductionmentioning

confidence: 99%

“…y-axis) lying in the same quadrant [8] and presented an O(nm) algorithm. They also considered the rectangle perimeter point labeling problem [9], in which the given elastic labels are to be placed on anchors that lie on the boundary of a given rectangular map. They combined the solution of the two-axis case and the twoparallel-line case to solve the rectangle perimeter point labeling problem in O(n…”

Section: Introductionmentioning

confidence: 99%

Labeling Points on a Single Line

Chen

Lee

Liao

2005

Int. J. Comput. Geom. Appl.

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In this paper, we consider a map labeling problem where the points to be labeled are restricted on a line. It is known that the 1d-4P and the 1d-4S unit-square label placement problem and the Slope-4P unit-square label placement problem can both be solved in linear time and the Slope-4S unit-square label placement problem can be solved in quadratic time in [7]. We extend the result to the following label placement problem: Slope-4P unit-height (width) label placement problem and elastic labels and present a linear time algorithm for it provided that the input points are given sorted. We further show that if the points are not sorted, the label placement problems have a lower bound of Ω(n log n), where n is the input size, under the algebraic computation tree model. Optimization versions of these point labeling problems are also considered.

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Elastic Labels Around the Perimeter of a Map

Cited by 10 publications

References 7 publications

Incremental labeling in closed-2PM model

Incremental labeling in closed-2PM model

Boundary Labeling: Models and Efficient Algorithms for Rectangular Maps

Labeling Points on a Single Line

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