Structure in Stable Matching Problems

dc.contributor.authorToth, William Justin
dc.date.accessioned2016-12-14T19:38:37Z
dc.date.available2016-12-14T19:38:37Z
dc.date.issued2016-12-14
dc.date.submitted2016-12-13
dc.description.abstractIn this thesis we provide two contributions to the study of structure in stable matching problems. The first contribution is a short new proof for the integrality of Rothblum’s linear description of the convex hull of incidence vectors of stable matchings in bipartite graphs. The key feature of our proof is to show that extreme points of the formulation must have a 0, 1-component. The second contribution is a computer search procedure for instances of cyclic stable matching problems with three genders as proposed by Knuth. We provide sufficient conditions for the existence of a stable matching in this context. We also investigate bijections of the problem instance vertex set to itself which preserve the set of stable matchings (up to permutation). Such bijections define “symmetric” problem instances. We study this notion of symmetry, and use it to cut down on the number of problem instances in our search. We implemented our proposed computational procedure in Java and end with a discussion of the results running computational experiments using our code on problem instances of size 5.en
dc.identifier.urihttp://hdl.handle.net/10012/11099
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectStable Matchingen
dc.subjectIterative Roundingen
dc.subjectCombinatorial Optimizationen
dc.titleStructure in Stable Matching Problemsen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degree.disciplineCombinatorics and Optimizationen
uws-etd.degree.grantorUniversity of Waterlooen
uws.contributor.advisorKoenemann, Jochen
uws.contributor.affiliation1Faculty of Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

Files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
Toth_WilliamJustin.pdf
Size:
458.93 KB
Format:
Adobe Portable Document Format
Description:

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
6.17 KB
Format:
Item-specific license agreed upon to submission
Description: