Piercing All Translates of a Set of Axis-Parallel Rectangles
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10486570" target="_blank" >RIV/00216208:11320/24:10486570 - isvavai.cz</a>
Výsledek na webu
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=-vP-Gt-2nw" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=-vP-Gt-2nw</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.37236/12041" target="_blank" >10.37236/12041</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Piercing All Translates of a Set of Axis-Parallel Rectangles
Popis výsledku v původním jazyce
For a given shape S in the plane, one can ask what is the lowest possible density of a point set P that pierces ("intersects", "hits") all translates of S. This is equivalent to determining the covering density of S and as such is well studied. Here we study the analogous question for families of shapes where the connection to covering is altered. That is, we require that a single point set P simultaneously pierces each translate of each shape from some family F. We denote the lowest possible density of such an F-piercing point set by pi(T)(F). Specifically, we focus on families F consisting of axis-parallel rectangles. When |F| = 2 we exactly solve the case when one rectangle is more squarish than 2 x 1, and give bounds (within 10 % of each other) for the remaining case when one rectangle is wide and the other one is tall. When |F| >= 2 we present a linear-time constant-factor approximation algorithm for computing pi(T)(F) (with ratio 1.895).
Název v anglickém jazyce
Piercing All Translates of a Set of Axis-Parallel Rectangles
Popis výsledku anglicky
For a given shape S in the plane, one can ask what is the lowest possible density of a point set P that pierces ("intersects", "hits") all translates of S. This is equivalent to determining the covering density of S and as such is well studied. Here we study the analogous question for families of shapes where the connection to covering is altered. That is, we require that a single point set P simultaneously pierces each translate of each shape from some family F. We denote the lowest possible density of such an F-piercing point set by pi(T)(F). Specifically, we focus on families F consisting of axis-parallel rectangles. When |F| = 2 we exactly solve the case when one rectangle is more squarish than 2 x 1, and give bounds (within 10 % of each other) for the remaining case when one rectangle is wide and the other one is tall. When |F| >= 2 we present a linear-time constant-factor approximation algorithm for computing pi(T)(F) (with ratio 1.895).
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2024
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Electronic Journal of Combinatorics
ISSN
1097-1440
e-ISSN
1077-8926
Svazek periodika
31
Číslo periodika v rámci svazku
1
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
16
Strana od-do
P1.33
Kód UT WoS článku
001167043200001
EID výsledku v databázi Scopus
2-s2.0-85184438277