Title:
Identity-Free Set Systems
Identity-Free Set Systems
Author(s)
Patel, Shyamal
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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.
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Date Issued
2020-05
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Text
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Undergraduate Thesis