Constrained Hitting Set Problem with Intervals

0548662 - ÚI 2022 RIV CH eng C - Konferenční příspěvek (zahraniční konf.)
Acharyya, Ankush - Keikha, Vahideh - Majumdar, D. - Pandit, S.
Constrained Hitting Set Problem with Intervals.
Computing and Combinatorics: 27th International Conference, COCOON 2021 Proceedings. Cham: Springer, 2021 - (Chen, C.; Hon, W.; Hung, L.; Lee, C.), s. 604-616. Lecture Notes in Computer Science, 13025. ISBN 978-3-030-89542-6. ISSN 0302-9743.
[COCOON 2021: International Conference on Computing and Combinatorics /27./. Tainan (TW), 24.10.2021-26.10.2021]
Grant CEP: GA ČR(CZ) GJ19-06792Y
Institucionální podpora: RVO:67985807
Klíčová slova: Fixed Parameter Tractability * Hitting Set Problem * Approximation Algorithm
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

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.
Trvalý link: http://hdl.handle.net/11104/0324711