TY - JOUR

T1 - Practical and efficient algorithms for the geometric hitting set problem

AU - Bus, Norbert

AU - Mustafa, Nabil H.

AU - Ray, Saurabh

N1 - Funding Information:
The work of Nabil H. Mustafa in this paper has been supported by the grant ANR SAGA ( JCJC-14-CE25-0016-01 ).
Publisher Copyright:
© 2017 Elsevier B.V.

PY - 2018/5/11

Y1 - 2018/5/11

N2 - The geometric hitting set problem is one of the basic geometric combinatorial optimization problems: given a set P of points and a set D of geometric objects in the plane, the goal is to compute a small-sized subset of P that hits all objects in D. Recently Agarwal and Pan (2014) presented a near-linear time algorithm for the case where D consists of disks in the plane. The algorithm uses sophisticated geometric tools and data structures with large resulting constants. In this paper, we design a hitting-set algorithm for this case without the use of these data-structures, and present experimental evidence that our new algorithm has near-linear running time in practice, and computes hitting sets within 1.3-factor of the optimal hitting set. We further present dnet, a public source-code module that incorporates this improvement, enabling fast and efficient computation of small-sized hitting sets in practice.

AB - The geometric hitting set problem is one of the basic geometric combinatorial optimization problems: given a set P of points and a set D of geometric objects in the plane, the goal is to compute a small-sized subset of P that hits all objects in D. Recently Agarwal and Pan (2014) presented a near-linear time algorithm for the case where D consists of disks in the plane. The algorithm uses sophisticated geometric tools and data structures with large resulting constants. In this paper, we design a hitting-set algorithm for this case without the use of these data-structures, and present experimental evidence that our new algorithm has near-linear running time in practice, and computes hitting sets within 1.3-factor of the optimal hitting set. We further present dnet, a public source-code module that incorporates this improvement, enabling fast and efficient computation of small-sized hitting sets in practice.

KW - Approximation algorithms

KW - Computational geometry

KW - Geometric hitting sets

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U2 - 10.1016/j.dam.2017.12.018

DO - 10.1016/j.dam.2017.12.018

M3 - Article

AN - SCOPUS:85040735765

VL - 240

SP - 25

EP - 32

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -