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On Realistic Line Simplification under Area Measure.

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Title: On Realistic Line Simplification under Area Measure.
Authors: Daneshpajouh, Shervin1 daneshpajouh@ce.sharif.edu, Zarei, Alireza1 zarei@mehr.sharif.edu, Ghodsi, Mohammad2 ghodsi@sharif.edu
Source: International MultiConference of Engineers & Computer Scientists 2009. 2009, p465-470. 6p. 5 Diagrams.
Subjects: Line geometry, Area measurement, Algorithms, Mathematical complexes, Geometry
Abstract: In this paper, we consider the well-known 2D line simplification problem under area measure. Primarily, we propose a unified definition for the area measure that can be used on a general path of n vertices. We present an O(n³) optimal simplification algorithm on general paths under unified area measure based on Imai and Iri's approach. Next, to improve the time complexity, we describe a realistic situation in which the path lies inside a bounded region. For such a realistic input path, we propose an ε-approximate algorithm of O( n²/ε) time complexity to find the simplification. We further define a variant of the area measure that overcomes the pitfalls of the common area measure arisen in degenerated cases. Our optimal or approximation algorithms can employ this measure at the same time and space complexities. Although, the area is the first natural simplification measure, to the best of our knowledge, the results presented here are the first sub-cubic simplification algorithms on this measure for general paths. [ABSTRACT FROM AUTHOR]
Copyright of International MultiConference of Engineers & Computer Scientists 2009 is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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An: 41021127
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  Data: On Realistic Line Simplification under Area Measure.
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  Data: <searchLink fieldCode="JN" term="%22International+MultiConference+of+Engineers+%26+Computer+Scientists+2009%22">International MultiConference of Engineers & Computer Scientists 2009</searchLink>. 2009, p465-470. 6p. 5 Diagrams.
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  Data: <searchLink fieldCode="DE" term="%22Line+geometry%22">Line geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Area+measurement%22">Area measurement</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+complexes%22">Mathematical complexes</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%22">Geometry</searchLink>
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  Data: In this paper, we consider the well-known 2D line simplification problem under area measure. Primarily, we propose a unified definition for the area measure that can be used on a general path of n vertices. We present an O(n³) optimal simplification algorithm on general paths under unified area measure based on Imai and Iri's approach. Next, to improve the time complexity, we describe a realistic situation in which the path lies inside a bounded region. For such a realistic input path, we propose an ε-approximate algorithm of O( n²/ε) time complexity to find the simplification. We further define a variant of the area measure that overcomes the pitfalls of the common area measure arisen in degenerated cases. Our optimal or approximation algorithms can employ this measure at the same time and space complexities. Although, the area is the first natural simplification measure, to the best of our knowledge, the results presented here are the first sub-cubic simplification algorithms on this measure for general paths. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of International MultiConference of Engineers & Computer Scientists 2009 is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 6
        StartPage: 465
    Subjects:
      – SubjectFull: Line geometry
        Type: general
      – SubjectFull: Area measurement
        Type: general
      – SubjectFull: Algorithms
        Type: general
      – SubjectFull: Mathematical complexes
        Type: general
      – SubjectFull: Geometry
        Type: general
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      – TitleFull: On Realistic Line Simplification under Area Measure.
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            NameFull: Daneshpajouh, Shervin
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            NameFull: Zarei, Alireza
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            NameFull: Ghodsi, Mohammad
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          Dates:
            – D: 01
              M: 01
              Text: 2009
              Type: published
              Y: 2009
          Titles:
            – TitleFull: International MultiConference of Engineers & Computer Scientists 2009
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