Line-Segment Intersection Made In-Place

We present a space-efficient algorithm for reporting all k intersections induced by a set of n line segments in the place. Our algorithm is an in-place variant of Balaban’s algorithm and runs in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{O}(n log^2_2 n + k)$\end{document} time using \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{O}$\end{document}(1) extra words of memory over and above the space used for the input to the algorithm.