On disjoint concave chains in arrangements of (pseudo) lines

Dan Halperin; Micha Sharir

doi:10.1016/0020-0190(94)00057-3

On disjoint concave chains in arrangements of (pseudo) lines

Dan Halperin^*
, Micha Sharir

^*Corresponding author for this work

School of Computer Science and AI

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In the paper mentioned in the title [1] we have asserted that the maximum number of edges of m pairwise-disjoint x-monotone concave polygonal chains, contained in the union of n lines or pseudo lines, is Θ(m^2/3n^2/3+n). While the assertion is correct, the analysis of [1] was incomplete, and hence erroneous. In this note we complete the analysis and thus obtain a correct proof of the assertion.

Original language	English
Pages (from-to)	53-56
Number of pages	4
Journal	Information Processing Letters
Volume	51
Issue number	1
DOIs	https://doi.org/10.1016/0020-0190(94)00057-3
State	Published - 12 Jul 1994

Keywords

Arrangements
Computational geometry
Polygonal chains

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10.1016/0020-0190(94)00057-3

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abstract = "In the paper mentioned in the title [1] we have asserted that the maximum number of edges of m pairwise-disjoint x-monotone concave polygonal chains, contained in the union of n lines or pseudo lines, is Θ(m2/3n2/3+n). While the assertion is correct, the analysis of [1] was incomplete, and hence erroneous. In this note we complete the analysis and thus obtain a correct proof of the assertion.",

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N2 - In the paper mentioned in the title [1] we have asserted that the maximum number of edges of m pairwise-disjoint x-monotone concave polygonal chains, contained in the union of n lines or pseudo lines, is Θ(m2/3n2/3+n). While the assertion is correct, the analysis of [1] was incomplete, and hence erroneous. In this note we complete the analysis and thus obtain a correct proof of the assertion.

AB - In the paper mentioned in the title [1] we have asserted that the maximum number of edges of m pairwise-disjoint x-monotone concave polygonal chains, contained in the union of n lines or pseudo lines, is Θ(m2/3n2/3+n). While the assertion is correct, the analysis of [1] was incomplete, and hence erroneous. In this note we complete the analysis and thus obtain a correct proof of the assertion.

KW - Arrangements

KW - Computational geometry

KW - Polygonal chains

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On disjoint concave chains in arrangements of (pseudo) lines

Abstract

Keywords

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