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Peeling Potatoes Near-optimally in Near-linear Time
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SYSNO ASEP 0478998 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Peeling Potatoes Near-optimally in Near-linear Time Tvůrce(i) Cabello, S. (SI)
Cibulka, J. (CZ)
Kynčl, J. (CZ)
Saumell, Maria (UIVT-O) RID, SAI, ORCID
Valtr, P. (CZ)Zdroj.dok. Siam Journal on Computing - ISSN 0097-5397
Roč. 46, č. 5 (2017), s. 1574-1602Poč.str. 29 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova geometric optimization ; potato peeling ; visibility graph ; geometric probability ; approximation algorithm Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics CEP GBP202/12/G061 GA ČR - Grantová agentura ČR Institucionální podpora UIVT-O - RVO:67985807 UT WOS 000416763900004 EID SCOPUS 85032943193 DOI https://doi.org/10.1137/16M1079695 Anotace We consider the following geometric optimization problem: find a convex polygon of maximum area contained in a given simple polygon $P$ with $n$ vertices. We give a randomized near-linear-time $(1-\varepsilon)$-approximation algorithm for this problem: in $O(n( \log^2 n + (1/\varepsilon^3) \log n + 1/\varepsilon^4))$ time we find a convex polygon contained in $P$ that, with probability at least $2/3$, has area at least $(1-\varepsilon)$ times the area of an optimal solution. We also obtain similar results for the variant of computing a convex polygon inside $P$ with maximum perimeter. To achieve these results we provide new results in geometric probability. The first result is a bound relating the area of the largest convex body inside $P$ to the probability that two points chosen uniformly at random inside $P$ are mutually visible. The second result is a bound on the expected value of the difference between the perimeter of any planar convex body $K$ and the perimeter of the convex hull of a uniform random sample inside $K$. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2018
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