Peeling Potatoes Near-optimally in Near-linear Time
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00478998" target="_blank" >RIV/67985807:_____/17:00478998 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/17:10366168
Result on the web
<a href="http://dx.doi.org/10.1137/16M1079695" target="_blank" >http://dx.doi.org/10.1137/16M1079695</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/16M1079695" target="_blank" >10.1137/16M1079695</a>
Alternative languages
Result language
angličtina
Original language name
Peeling Potatoes Near-optimally in Near-linear Time
Original language description
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 $K$.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Siam Journal on Computing
ISSN
0097-5397
e-ISSN
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Volume of the periodical
46
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
29
Pages from-to
1574-1602
UT code for WoS article
000416763900004
EID of the result in the Scopus database
2-s2.0-85032943193