Optimal point removal in closed-2PM labeling

Authors:
Farshad Rostamabadi;Iman Sadeghi;Mohammad Ghodsi;Ramtin Khosravi
Affiliations:
Computer Engineering Department, Sharif University of Technology, Tehran, Iran and School of Computer Science, Institute for Studies in Fundamental Sciences, Tehran, Iran;Computer Engineering Department, Sharif University of Technology, Tehran, Iran;Computer Engineering Department, Sharif University of Technology, Tehran, Iran and School of Computer Science, Institute for Studies in Fundamental Sciences, Tehran, Iran;Electrical and Computer Engineering Department, University of Tehran, Tehran, Iran
Venue:
Information Processing Letters
Year:
2008

Citing 3
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SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms

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Abstract

An optimal labeling where labels are disjoint axis-parallel equal-size squares is called 2PM labeling if the labels have maximum length each attached to its corresponding point on the middle of one of its horizontal edges. In a closed-2PM labeling, no two edges of labels containing points should intersect. Removing one point and its label, makes free room for its adjacent labels and may cause a global label expansion. In this paper, we construct several data structures in the preprocessing stage, so that any point removal event is handled efficiently. We present an algorithm which decides in O(lgn) amortized time whether a label removal leads to label expansion in which case a new optimal labeling for the remaining points is generated in O(n) amortized time.