New algorithms for two-label point labeling

Z. Qin, A. Wolff, Y.F. Xu, B. Zhu

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    14 Citations (Scopus)

    Abstract

    Given a label shape L and a set of n points in the plane, the 2-label point-labeling problem consists of placing 2n non-intersecting translated copies of L of maximum size such that each point touches two unique copies—its labels. In this paper we give new and simple approximation algorithms for L an axis-parallel square or a circle. For squares we improve the best previously known approximation factor from 1/3 to 1/2. For circles the improvement from 1/2 to ˜ 0.513 is less significant, but the fact that 1/2 is not best possible is interesting in its own right. For the decision version of the latter problem we have an NP-hardness proof that also shows that it is NP-hard to approximate the label size beyond a factor of ˜ 0.732. As their predecessors, our algorithms take O(n log n) time and O(n) space.
    Original languageEnglish
    Title of host publicationAlgorithms - ESA 2000 (Proceedings 8th Annual European Symposium, Saarbrücken, Germany, September 5-8, 2000)
    EditorsM. Paterson
    Place of PublicationBerlin
    PublisherSpringer
    Pages368-379
    ISBN (Print)3-540-41004-X
    DOIs
    Publication statusPublished - 2000

    Publication series

    NameLecture Notes in Computer Science
    Volume1879
    ISSN (Print)0302-9743

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