Cache-Oblivious Planar Shortest Paths

We present an efficient cache-oblivious implementation of the shortest-path algorithm for planar graphs by Klein et al., and prove that it incurs no more than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal O}(\frac{N}{B^{1/2 - \epsilon}} + \frac{N}{B}{\rm log}N$\end{document}) block transfers on a graph with N vertices. This is the first cache-oblivious algorithm for this problem that incurs o(N) block transfers.