Title:
Identity-Free Set Systems
Identity-Free Set Systems
| dc.contributor.author | Patel, Shyamal | |
| dc.contributor.committeeMember | Vempala, Santosh | |
| dc.contributor.committeeMember | Croot, Ernest | |
| dc.contributor.department | Computer Science | |
| dc.contributor.department | Computer Science | |
| dc.date.accessioned | 2020-11-09T17:01:19Z | |
| dc.date.available | 2020-11-09T17:01:19Z | |
| dc.date.created | 2020-05 | |
| dc.date.issued | 2020-05 | |
| dc.date.submitted | May 2020 | |
| dc.date.updated | 2020-11-09T17:01:19Z | |
| dc.description.abstract | Distance preservers are a fundamental primitive used to sketch graphs and finite metric spaces. Despite having a variety of applications, bounds on the size of distance preservers for weighted, directed, acyclic graphs remain unimproved for almost 15 years [Coppersmith and Elkin SIAM J. Disc. Math '06, Szemeredi and Trotter Combinatorica '83]. We describe a novel approach to improve bounds on distance preservers in this setting using path reroutings. This formulation of the problem circumvents a known technical lower bound [Bodwin and Williams SODA '16]. Moreover, we consider a number of closely related problems and give evidence that the upper bounds from [Coppersmith and Elkin SIAM J. Disc. Math '06] are not tight. | |
| dc.description.degree | Undergraduate | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1853/63897 | |
| dc.language.iso | en_US | |
| dc.publisher | Georgia Institute of Technology | |
| dc.subject | Distance preservers | |
| dc.subject | Sketching | |
| dc.subject | Extremal Combinatorics | |
| dc.subject | Additive Combinatoric | |
| dc.title | Identity-Free Set Systems | |
| dc.type | Text | |
| dc.type.genre | Undergraduate Thesis | |
| dspace.entity.type | Publication | |
| local.contributor.corporatename | College of Computing | |
| local.contributor.corporatename | School of Computer Science | |
| local.contributor.corporatename | Undergraduate Research Opportunities Program | |
| local.relation.ispartofseries | Undergraduate Research Option Theses | |
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| thesis.degree.level | Undergraduate |