Epsilon-approximations & epsilon-nets
NH Mustafa, K Varadarajan - Handbook of Discrete and …, 2017 - taylorfrancis.com
The use of random samples to approximate properties of geometric configurations has been
an influential idea for both combinatorial and algorithmic purposes. This chapter considers …
an influential idea for both combinatorial and algorithmic purposes. This chapter considers …
Efficient algorithms for discrepancy minimization in convex sets
A result of Spencer states that every collection of n sets over a universe of size n has a
coloring of the ground set with of discrepancy. A geometric generalization of this result was …
coloring of the ground set with of discrepancy. A geometric generalization of this result was …
[图书][B] Sampling in combinatorial and geometric set systems
NH Mustafa - 2022 - books.google.com
Understanding the behavior of basic sampling techniques and intrinsic geometric attributes
of data is an invaluable skill that is in high demand for both graduate students and …
of data is an invaluable skill that is in high demand for both graduate students and …
A simple proof of optimal epsilon nets
NH Mustafa, K Dutta, A Ghosh - Combinatorica, 2018 - Springer
A simple proof of optimal epsilon nets Page 1 COMBINATORICA Bolyai Society – Springer-Verlag
0209–9683/118/$6.00 c 2018 János Bolyai Mathematical Society and Springer-Verlag Berlin …
0209–9683/118/$6.00 c 2018 János Bolyai Mathematical Society and Springer-Verlag Berlin …
Shallow packings, semialgebraic set systems, Macbeath regions, and polynomial partitioning
Given a set system (X, R)(X, R) such that every pair of sets in RR have large symmetric
difference, the Shallow Packing Lemma gives an upper bound on| R|| R| as a function of the …
difference, the Shallow Packing Lemma gives an upper bound on| R|| R| as a function of the …
A simple proof of the shallow packing lemma
NH Mustafa - Discrete & Computational Geometry, 2016 - Springer
A Simple Proof of the Shallow Packing Lemma | SpringerLink Skip to main content
Advertisement SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home …
Advertisement SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home …
Two proofs for shallow packings
We refine the bound on the packing number, originally shown by Haussler, for shallow
geometric set systems. Specifically, let VV be a finite set system defined over an n-point set …
geometric set systems. Specifically, let VV be a finite set system defined over an n-point set …
Sparse Geometric Set Systems and the Beck-Fiala Conjecture
K Dutta, A Ghosh - arXiv preprint arXiv:2301.03329, 2023 - arxiv.org
We investigate the combinatorial discrepancy of geometric set systems having bounded
shallow cell complexity in the\emph {Beck-Fiala} setting, where each point belongs to at …
shallow cell complexity in the\emph {Beck-Fiala} setting, where each point belongs to at …
Output-sensitive tools for range searching in higher dimensions
M Sharir, S Zaban - arXiv preprint arXiv:1312.6305, 2013 - arxiv.org
Let $ P $ be a set of $ n $ points in ${\mathbb R}^{d} $. A point $ p\in P $ is $ k $\emph {-
shallow} if it lies in a halfspace which contains at most $ k $ points of $ P $(including $ p $) …
shallow} if it lies in a halfspace which contains at most $ k $ points of $ P $(including $ p $) …
Size sensitive packing number for Hamming cube and its consequences
K Dutta, A Ghosh - arXiv preprint arXiv:1412.3922, 2014 - arxiv.org
We prove a size-sensitive version of Haussler's Packing lemma~\cite {
Haussler92spherepacking} for set-systems with bounded primal shatter dimension, which …
Haussler92spherepacking} for set-systems with bounded primal shatter dimension, which …