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Author Mulzer, Wolfgang ♦ Rote, Gnter
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2008
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Optimal triangulations ♦ PLANAR 1-IN-3-SAT
Abstract A triangulation of a planar point set $\textit{S}$ is a maximal plane straight-line graph with vertex set $\textit{S}.$ In the minimum-weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge lengths. We prove that the decision version of this problem is NP-hard, using a reduction from PLANAR 1-IN-3-SAT. The correct working of the gadgets is established with computer assistance, using dynamic programming on polygonal faces, as well as the β-skeleton heuristic to certify that certain edges belong to the minimum-weight triangulation.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2008-05-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 55
Issue Number 2
Page Count 29
Starting Page 1
Ending Page 29


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Source: ACM Digital Library