Elastic Labels on the Perimeter of a Rectangle

Iturriaga, Claudia; Lubiw, Anna

doi:10.1007/3-540-37623-2_42

Cited by 1 publication

(1 citation statement)

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“…However, some polynomial time solvable versions of the map labeling problem have been considered [17]. 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%