Practical and efficient algorithms for the geometric hitting set problem

Norbert Bus, Nabil H. Mustafa, Saurabh Ray

    Research output: Contribution to journalArticle

    Abstract

    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.

    Original languageEnglish (US)
    Pages (from-to)25-32
    Number of pages8
    JournalDiscrete Applied Mathematics
    Volume240
    DOIs
    StatePublished - May 11 2018

    Fingerprint

    Hitting Set
    Efficient Algorithms
    Data structures
    Data Structures
    Combinatorial optimization
    Geometric Optimization
    Geometric object
    Linear-time Algorithm
    Combinatorial Optimization Problem
    Hits
    Linear Time
    Module
    Subset

    Keywords

    • Approximation algorithms
    • Computational geometry
    • Geometric hitting sets

    ASJC Scopus subject areas

    • Applied Mathematics
    • Discrete Mathematics and Combinatorics

    Cite this

    Practical and efficient algorithms for the geometric hitting set problem. / Bus, Norbert; Mustafa, Nabil H.; Ray, Saurabh.

    In: Discrete Applied Mathematics, Vol. 240, 11.05.2018, p. 25-32.

    Research output: Contribution to journalArticle

    Bus, Norbert ; Mustafa, Nabil H. ; Ray, Saurabh. / Practical and efficient algorithms for the geometric hitting set problem. In: Discrete Applied Mathematics. 2018 ; Vol. 240. pp. 25-32.
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