Peeling Potatoes Near-optimally in Near-linear Time

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/00216208:11320/17:10366168

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Peeling Potatoes Near-optimally in Near-linear Time

Popis výsledku v původním jazyce

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 $K$.

Název v anglickém jazyce

Peeling Potatoes Near-optimally in Near-linear Time

Popis výsledku anglicky

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 $K$.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Siam Journal on Computing

ISSN

0097-5397

e-ISSN

—

Svazek periodika

46

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

29

Strana od-do

1574-1602

Kód UT WoS článku

000416763900004

EID výsledku v databázi Scopus

2-s2.0-85032943193