The shortest watchtower and related problems for polyhedral terrains

Micha Sharir*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We present an O(n log2 n) algorithm for finding the shortest vertical segment ('watchtower') uv that has to be erected on a polyhedral terrain S with n faces, so that its top endpoint can see the entire terrain S. An extension of our technique yields an O(n log2 n + k) time algorithm for calculating the lower envelope of two polyhedral terrains, one of which is convex, where k is combinatorial complexity of the output envelope.

Original languageEnglish
Pages (from-to)265-270
Number of pages6
JournalInformation Processing Letters
Issue number5
StatePublished - 24 Nov 1988


FundersFunder number
Digital Equipment Corporation
IBM Corpora-tion
NCRD-the Israeli National Council for Research and Development
National Science FoundationNSF-DCR-83-20085
National Science Foundation
Office of Naval ResearchN00014-82-K-0381
Office of Naval Research


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