Incremental labeling in closed-2PM model

Authors:
Farshad Rostamabadi;Mohammad Ghodsi
Affiliations:
Department of Computer Engineering, Sharif University of Technology, P.O. Box 11365-9415, Tehran, Iran and School of Computer Science, Institute for Studies in Fundamental Sciences (IPM), P.O. Box ...;Department of Computer Engineering, Sharif University of Technology, P.O. Box 11365-9415, Tehran, Iran and School of Computer Science, Institute for Studies in Fundamental Sciences (IPM), P.O. Box ...
Venue:
Computers and Electrical Engineering
Year:
2010

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Abstract

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(lgn+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.