The Maximum Anchored k-core Problem: Mixed Integer Programming Formulations

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dc.contributor.advisorHicks, Illya V
dc.creatorKroger, Samuel
dc.date.accessioned2022-10-05T21:28:53Z
dc.date.available2022-10-05T21:28:53Z
dc.date.created2022-05
dc.date.issued2022-04-14
dc.date.submittedMay 2022
dc.date.updated2022-10-05T21:28:53Z
dc.description.abstractThe maximum anchored k-core problem plays an important role in marketing, network architecture, and social media; the problem allows network designers and influencers to find the most pivotal vertices which increase the size of the network. In this thesis, we investigate two mixed integer programming (MIP) formulations for the maximum anchored k-core problem: (i) a naive model and (ii) a strong model. We examine the MIP formulations analytically and computationally. We also compare the computational performance of the MIP models with two existing heuristic algorithms: Residual Core Maximization (RCM) and Onion-Layer based Anchored k-core (OLAK). Furthermore, we propose valid inequalities and fixing procedures to improve the computational performance of the MIP models. Finally, we conduct experiments on a set of benchmark instances. Our computational experiments show the superiority of the strong model against the naive model, and the heuristics.
dc.format.mimetypeapplication/pdf
dc.identifier.citationKroger, Samuel. "The Maximum Anchored k-core Problem: Mixed Integer Programming Formulations." (2022) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/113532">https://hdl.handle.net/1911/113532</a>.
dc.identifier.urihttps://hdl.handle.net/1911/113532
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectk-core
dc.subjectmixed integer programming
dc.subjectfacet defining inequalities
dc.titleThe Maximum Anchored k-core Problem: Mixed Integer Programming Formulations
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Arts
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