Computing Largest Minimum Color-Spanning Intervals of Imprecise Points

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F24%3A00585146" target="_blank" >RIV/67985807:_____/24:00585146 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-3-031-55598-5_6" target="_blank" >http://dx.doi.org/10.1007/978-3-031-55598-5_6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-55598-5_6" target="_blank" >10.1007/978-3-031-55598-5_6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Computing Largest Minimum Color-Spanning Intervals of Imprecise Points

Popis výsledku v původním jazyce

We study a geometric facility location problem under imprecision. Given n unit intervals in the real line, each with one of k colors, the goal is to place one point in each interval such that the resulting minimum color-spanning interval is as large as possible. A minimum color-spanning interval is an interval of minimum size that contains at least one point from a given interval of each color. We prove that if the input intervals are pairwise disjoint, the problem can be solved in O (n) time, even for intervals of arbitrary length. For overlapping intervals, the problem becomes much more difficult. Nevertheless, we show that it can be solved in O (n2 log n) time when k = 2, by exploiting several structural properties of candidate solutions, combined with a number of advanced algorithmic techniques. Interestingly, this shows a sharp contrast with the 2-dimensional version of the problem, recently shown to be NP hard.

Název v anglickém jazyce

Computing Largest Minimum Color-Spanning Intervals of Imprecise Points

Popis výsledku anglicky

We study a geometric facility location problem under imprecision. Given n unit intervals in the real line, each with one of k colors, the goal is to place one point in each interval such that the resulting minimum color-spanning interval is as large as possible. A minimum color-spanning interval is an interval of minimum size that contains at least one point from a given interval of each color. We prove that if the input intervals are pairwise disjoint, the problem can be solved in O (n) time, even for intervals of arbitrary length. For overlapping intervals, the problem becomes much more difficult. Nevertheless, we show that it can be solved in O (n2 log n) time when k = 2, by exploiting several structural properties of candidate solutions, combined with a number of advanced algorithmic techniques. Interestingly, this shows a sharp contrast with the 2-dimensional version of the problem, recently shown to be NP hard.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název statě ve sborníku

LATIN 2024: Theoretical Informatics. Proceedings, part I

ISBN

978-3-031-55597-8

ISSN

—

e-ISSN

—

Počet stran výsledku

16

Strana od-do

81-96

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Puerto Varas

Datum konání akce

18. 3. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001214186800006