Constrained Hitting Set Problem with Intervals

Authors: Ankush Acharyya, Vahideh Keikha, D. Majumdar, S. Pandit
Publication year: 2021
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Computing and Combinatorics: 27th International Conference, COCOON 2021 Proceedings
Projects: Structural properties of visibility in terrains and farthest color Voronoi diagrams
Bibliographic citation: ACHARYYA, Ankush, KEIKHA, Vahideh, MAJUMDAR, D., PANDIT, S. Constrained Hitting Set Problem with Intervals. In: CHEN, Ch.-Y., HON, W.-K., HUNG, L.-J., LEE, Ch.-W., eds. Computing and Combinatorics: 27th International Conference, COCOON 2021 Proceedings. Cham: Springer, 2021, S. 604-616. Lecture Notes in Computer Science, 13025. ISBN 978-3-030-89542-6. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-030-89543-3_50
DOI: 10.1007/978-3-030-89543-3_50
ID: 548662

Abstract

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.