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- W2617996878 abstract "We revisit the following problem: Given a convex polygon $P$, find the largest-area inscribed triangle. We show by example that the linear-time algorithm presented in 1979 by Dobkin and Snyder for solving this problem fails. We then proceed to show that with a small adaptation, their approach does lead to a quadratic-time algorithm. We also present a more involved $O(nlog n)$ time divide-and-conquer algorithm. Also we show by example that the algorithm presented in 1979 by Dobkin and Snyder for finding the largest-area $k$-gon that is inscribed in a convex polygon fails to find the optimal solution for $k=4$. Finally, we discuss the implications of our discoveries on the literature." @default.
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- W2617996878 date "2020-09-01" @default.
- W2617996878 modified "2023-09-24" @default.
- W2617996878 title "Maximum-area triangle in a convex polygon, revisited" @default.
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- W2617996878 doi "https://doi.org/10.1016/j.ipl.2020.105943" @default.
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