A New Approximation Algorithm for k-Set Cover Problem

Essa, Hanaa A. E.; El-Latif, Yasser M. Abd; Ali, Salwa M.; Khamis, Soheir M.

doi:10.1007/s13369-015-1895-3

Cited by 1 publication

(1 citation statement)

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“…Specifically, the maximum set K-covering problem (MKCP) consists in selecting a subset of K columns from a given set of n columns, in such a way that the number of rows covered by the selected columns is maximized (see Lin and Guan [3]). Another related problem is the K-set cover problem (K-scp) that seeks to cover all rows of a matrix with the minimum number of columns such that each column chosen can cover at most K rows (see HAE, et al [4]).…”

Section: Introductionmentioning

confidence: 99%

A Simple and Effective Methodology for Generating Bounded Solutions for the Set K-Covering and Set Variable K-Covering Problems: A Guide for or Practitioners

McNally¹,

Lu²,

Shively-Ertas³

et al. 2021

Review of Computer Engineering Research

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As generalizations of the classic set covering problem (SCP), both the set K-covering problem (SKCP) and the set variable (K varies by constraint) K-covering problem (SVKCP) are easily shown to be NP-hard. Solution approaches in the literature for the SKCP typically provide no guarantees on solution quality. In this article, a simple methodology, called the simple sequential increasing tolerance (SSIT) matheuristic, that iteratively uses any general-purpose integer programming software (Gurobi and CPLEX in this case) is discussed. This approach is shown to quickly generate solutions that are guaranteed to be within a tight tolerance of the optimum for 135 SKCPs (average of 67 seconds on a standard PC and at most 0.13% from the optimums) from the literature and 65 newly created SVKCPs. This methodology generates solutions that are guaranteed to be within a specified percentage of the optimum in a short time (actual deviation from the optimums for the 135 SKCPs was 0.03%). Statistical analyses among the five best SKCP algorithms and SSIT demonstrates that SSIT performs as well as the best published algorithms designed specifically to solve SKCPs and SSIT requires no time-consuming effort of coding problem-specific algorithms-a real plus for OR practitioners.Contribution/Originality: This study documents a methodology that iteratively uses integer programming software to efficiently generate solutions that are guaranteed to be very close to the optimums for the set Kcovering problem. A significant benefit of this methodology is that no problem specific algorithm needs to be coded by the user.

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Section: Introductionmentioning

confidence: 99%