On a posterior evaluation of a simple greedy method for set packing

Kwon, Roy H.; Dalakouras, Georgios Vasileiou; Wang, Cheng

doi:10.1007/s11590-008-0085-6

Cited by 5 publications

(4 citation statements)

References 8 publications

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“…Landete et al (2013) proposed alternate formulations for SPP in higher dimensions and then added valid inequalities that were facets to the lifted polytope. Kwon et al (2008) and Kolokolov and Zaozerskaya (2009) also proposed new facets that strengthen the relaxed formulations of SPP. Li et al (2020) encoded SPP as a maximum weighted independent set and then used a Diversion Local Search based on the Weighted Configuration Checking (DLSWCC) algorithm to solve it.…”

Section: Phase 2: Set Packingmentioning

confidence: 99%

xER: An Explainable Model for Entity Resolution using an Efficient Solution for the Clique Partitioning Problem

Vadrevu¹,

Nagi²,

Xiong³

et al. 2021

Proceedings of the First Workshop on Trustworthy Natural Language Processing

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In this paper, we propose a global, selfexplainable solution to solve a prominent NLP problem: Entity Resolution (ER). We formulate ER as a graph partitioning problem. Every mention of a real-world entity is represented by a node in the graph, and the pairwise similarity scores between the mentions are used to associate these nodes to exactly one clique, which represents a real-world entity in the ER domain. In this paper, we use Clique Partitioning Problem (CPP), which is an Integer Program (IP) to formulate ER as a graph partitioning problem and then highlight the explainable nature of this method. Since CPP is NP-Hard, we introduce an efficient solution procedure, the xER algorithm, to solve CPP as a combination of finding maximal cliques in the graph and then performing generalized set packing using a novel formulation. We discuss the advantages of using xER over the traditional methods and provide the computational experiments and results of applying this method to ER data sets.

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Section: Phase 2: Set Packingmentioning

confidence: 99%

xER: An Explainable Model for Entity Resolution using an Efficient Solution for the Clique Partitioning Problem

Vadrevu¹,

Nagi²,

Xiong³

et al. 2021

Proceedings of the First Workshop on Trustworthy Natural Language Processing

View full text Add to dashboard Cite

show abstract

“…It is useful to formulate, when it is possible, discrete optimization problems as integer linear programming models, in order to use different well-known optimization techniques for their solving [22,23,34]. Following that idea a GAs is used on the mixed integer linear programming formulation for the MHS described below.…”

Section: Mathematical Modelmentioning

confidence: 99%

A genetic algorithm for the minimum hitting set

Cendic-Lazovic¹

2014

Sci Publ State Univ Novi Pazar Ser A

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In this paper the Minimum Hitting Set (MHS) problem is considered. The problem is solved by a genetic algorithms (GA) that uses binary encoding and standard genetics operators adapted to the problem. In proposed implementation all individuals are feasibility by default, so search is directed into the promising regions. The overall performance of the GA implementation is improved by caching technique. Local search optimization is used to refine the solutions explored by GAs. The algorithm is tested on standard instances from the literature. The obtained results are also compared with the results of existing methods for solving MHS in order to assess their merits.

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“…It is useful to formulate, when it is possible, discrete optimization problems as integer or mixed integer programming models, in order to use different well-known optimization techniques for their solving [16,17,21]. Following that idea we have used the CPLEX solver on the new integer linear programming formulation for the MSSP described below.…”

Section: An Integer Linear Programming Formulationmentioning

confidence: 99%

An integer linear programming formulation and genetic algorithm for the maximum set splitting problem

Lazović

Marić

Filipović

et al. 2012

Publ Inst Math (Belgr)

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We consider the maximum set splitting problem (MSSP). For the first time an integer linear programming (ILP) formulation is presented and validity of this formulation is given. We propose a genetic algorithm (GA) that uses the binary encoding and the standard genetic operators adapted to the problem. The overall performance of the GA implementation is improved by a caching technique. Experimental results are performed on two sets of instances from the literature: minimum hitting set and Steiner triple systems. The results show that CPLEX optimally solved all hitting set instances up to 500 elements and 10000 subsets. Also, it can be seen that GA routinely reached all optimal solutions up to 500 elements and 50000 subsets. The Steiner triple systems seems to be much more challenging for maximum set splitting problems since the CPLEX solved to optimality, within two hours, only two instances up to 15 elements and 35 subsets. For these instances GA reached all solutions as CPLEX but in much smaller running time.

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On a posterior evaluation of a simple greedy method for set packing

Cited by 5 publications

References 8 publications

xER: An Explainable Model for Entity Resolution using an Efficient Solution for the Clique Partitioning Problem

xER: An Explainable Model for Entity Resolution using an Efficient Solution for the Clique Partitioning Problem

A genetic algorithm for the minimum hitting set

An integer linear programming formulation and genetic algorithm for the maximum set splitting problem

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