The widely known linear time algorithm for computing the maximum area
triangle in a convex polygon was found incorrect recently by Keikha et.
al.(arXiv:1705.11035). We present an alternative algorithm in this paper.
Comparing to the only previously known correct solution, ours is much simpler
and more efficient. More importantly, our new approach is powerful in solving
related problems

Jin, Kai

English

arXiv

We propose a new technique called Rotate-and-Kill for solving the polygon
inclusion and circumscribing problems. By applying this technique, we obtain
$O(n)$ time algorithms for computing (1) the maximum area triangle in a given
$n$-sided convex polygon $P$, (2) the minimum area triangle enclosing $P$, (3)
the minimum area triangle enclosing $P$ touching edge-to-edge, i.e. the minimum
area triangle that is the intersection of three half-planes out of the $n$
half-planes defining $P$, and (4) the minimum perimeter triangle enclosing $P$
touching edge-to-edge. Our algorithm for computing the maximum area triangle is
simpler than its alternatives given in [Chandran and Mount, IJCGA'92] and
[Kallus, arXiv'17]. Our algorithms for computing the minimum area or perimeter
triangle enclosing $P$ touching edge-to-edge improve the $O(n\log n)$ or
$O(n\log^2n)$ time algorithms given in [Boyce \emph{et al.}, STOC'82],
[Aggarwal \emph{et al.}, Algorithmica'87], [Aggarwal and J. Park., FOCS'88],
[Aggarwal \emph{et al.}, DCG'94], and [Schieber, SODA'95]

Maximal Area Triangles in a Convex Polygon

Abstract

Similar works

Full text

Available Versions

arXiv.org e-Print Archive