An improved upper bound on the number of intersections between two rectangular paths
type: Item
instance of: scholarly article
title: An improved upper bound on the number of intersections between two rectangular paths
zbMATH Open document ID: 0724.68093
DOI: 10.1016/0020-0190(91)90146-9
author: Kim-Heng Teo
author: Tai-Ching Tuan
published in: Information Processing Letters
publication date: 1991-01-01T00:00:00Z
review text: Let I(P,Q) be the number of intersections between two rectangular paths P and Q. \textit{K. Kant} [IEEE Trans. Comput. C-34, 1045-1049 (1985; Zbl 0572.68057)] shows that \[ I(P,Q)\leq \frac{10}{9}| P| | Q| +\frac{4}{9}(| P| +| Q|). \] Recently, Wang et al. improved the upper bound to \[ | P| | Q| +\frac{1}{2}\min \{| P|,| Q| \}+\frac{1}{3}\max \{| P|,| Q| \} \] and conjecture that the bound cao be further sharpened to \(| P| | Q| +2\) for \(2\leq \min \{| P|,| Q| \}.\) An upper bound on I(P,Q), where both P and Q restricted to be monotonic, is derived, the conjecture of \textit{Y. L. Wang}, \textit{R. C. T. Lee} and \textit{J. S. Chang} [The number of intersections between two rectangular paths, IEEE Trans. Comput. 38, 1564-1571 (1989)] is validated.
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 68Q25
zbMATH DE Number: 4195228
zbMATH Keywords: interference
zbMATH Keywords: VLSI layout
zbMATH Keywords: intersections
zbMATH Keywords: rectangular paths
zbMATH Keywords: upper bound
MaRDI profile type: Publication
full work available at URL: 0020-0190(91)90146-9
OpenAlex ID: W2070379127
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cites work: The number of intersections between two rectangular paths
description: scientific article; zbMATH DE number 4195228