Minimum Enclosing Circle with Few Extra Variables

Authors Minati De, Subhas C. Nandy, Sasanka Roy

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Minati De
Subhas C. Nandy
Sasanka Roy

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Minati De, Subhas C. Nandy, and Sasanka Roy. Minimum Enclosing Circle with Few Extra Variables. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 510-521, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


Asano et al. [JoCG 2011] proposed an open problem of computing the minimum enclosing circle of a set of n points in R^2 given in a read-only array in sub-quadratic time. We show that Megiddo's prune and search algorithm for computing the minimum radius circle enclosing the given points can be tailored to work in a read-only environment in O(n^{1+epsilon}) time using O(log n) extra space, where epsilon is a positive constant less than 1. As a warm-up, we first solve the same problem in an in-place setup in linear time with O(1) extra space.
  • Minimum enclosing circle
  • space-efficient algorithm
  • prune-and-search


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