Constrained hitting set problem with intervals: Hardness, FPT and approximation algorithms

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F24%3A00585147" target="_blank" >RIV/67985807:_____/24:00585147 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1016/j.tcs.2024.114402" target="_blank" >https://doi.org/10.1016/j.tcs.2024.114402</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.tcs.2024.114402" target="_blank" >10.1016/j.tcs.2024.114402</a>

Result language

angličtina

Original language name

Constrained hitting set problem with intervals: Hardness, FPT and approximation algorithms

Original language description

We study a constrained version of the Geometric Hitting Set problem where we are given a set of points, partitioned into pairwise 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, we must select all the points from that subset. 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. On the contrary, if each subset contains at most t points, where t >= 2, and the intervals are overlapping, we show that the problem becomes NP-Hard. Further, when each subset contains at most t points where t >= 3, and the intervals are disjoint, we prove that the problem is NP-Hard, and we provide two constant factor approximation algorithms for this problem. We also study the problem from the parameterized complexity perspective. If the intervals are disjoint, then 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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

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

Project

<a href="/en/project/GJ19-06792Y" target="_blank" >GJ19-06792Y: Structural properties of visibility in terrains and farthest color Voronoi diagrams</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

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

Name of the periodical

Theoretical Computer Science

ISSN

0304-3975

e-ISSN

1879-2294

Volume of the periodical

990

Issue of the periodical within the volume

1 April 2024

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

16

Pages from-to

114402

UT code for WoS article

001174592700001

EID of the result in the Scopus database

2-s2.0-85183578352