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Sampling in Combinatorial and Geometric Set Systems
About this Title
Nabil H. Mustafa, Université Sorbonne Paris Nord, Villetaneuse, France
Publication: Mathematical Surveys and Monographs
Publication Year:
2022; Volume 265
ISBNs: 978-1-4704-6156-0 (print); 978-1-4704-6873-6 (online)
DOI: https://doi.org/10.1090/surv/265
Table of Contents
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Front/Back Matter
Chapters
- A probabilistic averaging technique
- First constructions of epsilon-nets
- Refining random samples
- Complexity of set systems
- Packings of set systems
- Epsilon-nets: Combinatorial bounds
- Epsilon-nets: An algorithm
- Epsilon-nets: Weighted case
- Epsilon-nets: Convex sets
- VC-dimension of $k$-fold unions: Basic case
- VC-dimension of $k$-fold unions: General case
- Epsilon-approximations: First bounds
- Epsilon-approximations: Improved bounds
- Epsilon-approximations: Relative case
- Epsilon-approximations: Functional case
- A summary of known bounds
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