On Realistic Line Simplification under Area Measure.

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Bibliographic Details
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]
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Database:	Engineering Source

Description
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]