Computing external farthest neighbors for a simple polygon

Pankaj K. Agarwal, Alok Aggarwal, Boris Aronov, S. Rao Kosaraju, Baruch Schieber, Subhash Suri

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Let P be (the boundary of) a simple polygon with n vertices. For a vertex p of P, let φ{symbol}(p) be the set of points on P that are farthest from p, where the distance between two points is the length of the (Euclidean) shortest path that connects them without intersecting the interior of P. In this paper, we present an O(n log n) algorithm to compute a member of φ{symbol}(p) for every vertex p of P. As a corollary, the external diameter of P can also be computed in the same time.

Original languageEnglish (US)
Pages (from-to)97-111
Number of pages15
JournalDiscrete Applied Mathematics
Issue number2
StatePublished - Apr 15 1991
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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