Related papers: Differentially Private All-Pairs Shortest Distance…
We study the problem of differentially private optimization with linear constraints when the right-hand-side of the constraints depends on private data. This type of problem appears in many applications, especially resource allocation.…
To expand the toolbox available to network science, we study the isomorphism between distance and Fuzzy (proximity or strength) graphs. Distinct transitive closures in Fuzzy graphs lead to closures of their isomorphic distance graphs with…
In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower…
Given a digraph $D$, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in $D$ an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree 0. Gutin, Razgon and Kim (2008) proved that…
We propose differentially private algorithms for parameter estimation in both low-dimensional and high-dimensional sparse generalized linear models (GLMs) by constructing private versions of projected gradient descent. We show that the…
In this paper, we develop a theory of new classes of discrete convex functions, called L-extendable functions and alternating L-convex functions, defined on the product of trees. We establish basic properties for optimization: a…
In the era of big data, the need to expand the amount of data through data sharing to improve model performance has become increasingly compelling. As a result, effective collaborative learning models need to be developed with respect to…
Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More…
Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…
We study differentially private algorithms for analyzing graphs in the challenging setting of continual release with fully dynamic updates, where edges are inserted and deleted over time, and the algorithm is required to update the solution…
In this work, we propose a differentially private algorithm for publishing matrices aggregated from sparse vectors. These matrices include social network adjacency matrices, user-item interaction matrices in recommendation systems, and…
We study the problem of performing counting queries at different levels in hierarchical structures while preserving individuals' privacy. Motivated by applications, we propose a new error measure for this problem by considering a…
We present the first non-trivial algorithm for the all-pairs minimum cut problem in the cut-query model. Given cut-query access to an unweighted graph $G=(V,E)$ with $n$ vertices, our randomized algorithm constructs a Gomory-Hu tree of $G$,…
Given a graph, the sparsest cut problem asks for a subset of vertices whose edge expansion (the normalized cut given by the subset) is minimized. In this paper, we study a generalization of this problem seeking for $ k $ disjoint subsets of…
We introduce efficient differentially private (DP) algorithms for several linear algebraic tasks, including solving linear equalities over arbitrary fields, linear inequalities over the reals, and computing affine spans and convex hulls. As…
A large number of NP-hard graph problems can be solved in $f(w)n^{O(1)}$ time and space when the input graph is provided together with a tree decomposition of width $w$, in many cases with a modest exponential dependence $f(w)$ on $w$.…
We introduce an $(\epsilon, \delta)$-jointly differentially private algorithm for packing problems. Our algorithm not only achieves the optimal trade-off between the privacy parameter $\epsilon$ and the minimum supply requirement (up to…
In length-constrained minimum spanning tree (MST) we are given an $n$-node graph $G = (V,E)$ with edge weights $w : E \to \mathbb{Z}_{\geq 0}$ and edge lengths $l: E \to \mathbb{Z}_{\geq 0}$ along with a root node $r \in V$ and a…
Fingerprinting arguments, first introduced by Bun, Ullman, and Vadhan (STOC 2014), are the most widely used method for establishing lower bounds on the sample complexity or error of approximately differentially private (DP) algorithms.…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…