Constrained Hitting Set Problem with Intervals

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00548662" target="_blank" >RIV/67985807:_____/21:00548662 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-3-030-89543-3_50" target="_blank" >http://dx.doi.org/10.1007/978-3-030-89543-3_50</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-89543-3_50" target="_blank" >10.1007/978-3-030-89543-3_50</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Constrained Hitting Set Problem with Intervals

Popis výsledku v původním jazyce

We study a constrained version of the Geometric Hitting Set problem where we are given a set of points, partitioned into disjoint subsets, and a set of intervals. The objective is to hit all the intervals with a minimum number of points such that if we select a point from a subset then we must select all the points from that subset. In general, when the intervals are disjoint, we prove that the problem is in FPT, when parameterized by the size of the solution. We also complement this result by giving a lower bound in the size of the kernel for disjoint intervals, and we also provide a polynomial kernel when the size of all subsets is bounded by a constant. Next, we consider two special cases of the problem where each subset can have at most 2 and 3 points. If each subset contains at most 2 points and the intervals are disjoint, we show that the problem admits a polynomial-time algorithm. However, when each subset contains at most 3 points and intervals are disjoint, we prove that the problem is NP-Hard and we provide two constant factor approximations for the problem.

Název v anglickém jazyce

Constrained Hitting Set Problem with Intervals

Popis výsledku anglicky

We study a constrained version of the Geometric Hitting Set problem where we are given a set of points, partitioned into disjoint subsets, and a set of intervals. The objective is to hit all the intervals with a minimum number of points such that if we select a point from a subset then we must select all the points from that subset. In general, when the intervals are disjoint, we prove that the problem is in FPT, when parameterized by the size of the solution. We also complement this result by giving a lower bound in the size of the kernel for disjoint intervals, and we also provide a polynomial kernel when the size of all subsets is bounded by a constant. Next, we consider two special cases of the problem where each subset can have at most 2 and 3 points. If each subset contains at most 2 points and the intervals are disjoint, we show that the problem admits a polynomial-time algorithm. However, when each subset contains at most 3 points and intervals are disjoint, we prove that the problem is NP-Hard and we provide two constant factor approximations for the problem.

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

<a href="/cs/project/GJ19-06792Y" target="_blank" >GJ19-06792Y: Strukturální vlastnosti viditelnosti terénů a Voroného diagramů nejvzdálenější barvy</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název statě ve sborníku

Computing and Combinatorics: 27th International Conference, COCOON 2021 Proceedings

ISBN

978-3-030-89542-6

ISSN

0302-9743

e-ISSN

—

Počet stran výsledku

13

Strana od-do

604-616

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Tainan

Datum konání akce

24. 10. 2021

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000767965300050