Alternative formulations for the Set Packing Problem and their application to the Winner Determination Problem

Landete, Mercedes; Monge, Juan F.; Rodríguez‐Chía, Antonio M.

doi:10.1007/s10479-011-1039-4

Cited by 4 publications

(4 citation statements)

References 22 publications

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“…Rossi and Smriglio (2001) proposed a branch-and-cut approach for solving the SPP. 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.…”

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

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show abstract

Section: Phase 2: Set Packingmentioning

confidence: 99%

Proceedings of the First Workshop on Trustworthy Natural Language Processing

2021

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We introduce a method that transforms a rulebased relation extraction (RE) classifier into a neural one such that both interpretability and performance are achieved. Our approach jointly trains a RE classifier with a decoder that generates explanations for these extractions, using as sole supervision a set of rules that match these relations. Our evaluation on the TACRED dataset shows that our neural RE classifier outperforms the rule-based one we started from by 9 F1 points; our decoder generates explanations with a high BLEU score of over 90%; and, the joint learning improves the performance of both the classifier and decoder.

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“…Landete et al [24] present an alternative formulation for the SPP in a higher-dimensional space where a set of facets can be identified.…”

Section: The Set Packing Problem (Spp)mentioning

confidence: 99%

A fast approximation algorithm for solving the complete set packing problem

Nguyen

2014

European Journal of Operational Research

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We study the complete set packing problem (CSPP) where the family of feasible subsets may include all possible combinations of objects. This setting arises in applications such as combinatorial auctions (for selecting optimal bids) and cooperative game theory (for finding optimal coalition structures). Although the set packing problem has been well-studied in the literature, where exact and approximation algorithms can solve very large instances with up to hundreds of objects and thousands of feasible subsets, these methods are not extendable to the CSPP since the number of feasible subsets is exponentially large. Formulating the CSPP as an MILP and solving it directly, using CPLEX for example, is impossible for problems with more than 20 objects. We propose a new mathematical formulation for the CSPP that directly leads to an efficient algorithm for finding feasible set packings (upper bounds). We also propose a new formulation for finding tighter lower bounds compared to LP relaxation and develop an efficient method for solving the corresponding large-scale MILP. We test the algorithm with the winner determination problem in spectrum auctions, the coalition structure generation problem in coalitional skill games, and a number of other simulated problems that appear in the literature.

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Alternative formulations for the Set Packing Problem and their application to the Winner Determination Problem

Cited by 4 publications

References 22 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

Proceedings of the First Workshop on Trustworthy Natural Language Processing

A fast approximation algorithm for solving the complete set packing problem

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