Geometric data summarization has become an essential tool in both geometric
approximation algorithms and where geometry intersects with big data problems. In linear or …

A central problem in computational geometry, range searching arises in many applications,
and numerous geometric problems can be formulated in terms of range searching. A typical …

We study trade-offs between accuracy and privacy in the context of linear queries over
histograms. This is a rich class of queries that includes contingency tables and range …

We study the mergeability of data summaries. Informally speaking, mergeability requires
that, given two summaries on two datasets, there is a way to merge the two summaries into a …

A central problem in computational geometry, range searching arises in many applications,
and a variety of geometric problems can be formulated as range-searching problems. A …

An important result in discrepancy due to Banaszczyk states that for any set of n vectors in ℝ
m of ℓ2 norm at most 1 and any convex body K in ℝ m of Gaussian measure at least half …

Let P be a set of n points in R^d. We present a linear-size data structure for answering range
queries on P with constant-complexity semialgebraic sets as ranges, in time close to O(n^1 …

The partial coloring method is one of the most powerful and widely used method in
combinatorial discrepancy problems. However, in many cases it leads to sub-optimal …

US9672364B2 - Differentially private linear queries on histograms - Google Patents
US9672364B2 - Differentially private linear queries on histograms - Google Patents Differentially …

The concept of matrix rigidity was introduced by Valiant (independently by Grigoriev) in the
context of computing linear transformations. A matrix is rigid if it is far (in terms of Hamming …