Related papers: The Discrepancy of Shortest Paths
The $\mathsf{HYBRID}$ model, introduced in [Augustine et al., SODA '20], provides a theoretical foundation for networks that allow multiple communication modes. The model follows the principles of synchronous message passing, whereas nodes…
We study the reverse shortest path problem on disk graphs in the plane. In this problem we consider the proximity graph of a set of $n$ disks in the plane of arbitrary radii: In this graph two disks are connected if the distance between…
In discrepancy minimization problems, we are given a family of sets $\mathcal{S} = \{S_1,\dots,S_m\}$, with each $S_i \in \mathcal{S}$ a subset of some universe $U = \{u_1,\dots,u_n\}$ of $n$ elements. The goal is to find a coloring $\chi :…
A hereditary property of graphs is a collection of graphs which is closed under taking induced subgraphs. The speed of \P is the function n \mapsto |\P_n|, where \P_n denotes the graphs of order n in \P. It was shown by Alekseev, and by…
Fingerprinting codes are a crucial tool for proving lower bounds in differential privacy. They have been used to prove tight lower bounds for several fundamental questions, especially in the ``low accuracy'' regime. Unlike…
The approximate single-source shortest-path problem is as follows: given a graph with nonnegative edge weights and a designated source vertex $s$, return estimates of the distances from~$s$ to each other vertex such that the estimate falls…
Let $(X,\S)$ be a set system on an $n$-point set $X$. The \emph{discrepancy} of $\S$ is defined as the minimum of the largest deviation from an even split, over all subsets of $S \in \S$ and two-colorings $\chi$ on $X$. We consider the…
Densest subgraph detection is a fundamental graph mining problem, with a large number of applications. There has been a lot of work on efficient algorithms for finding the densest subgraph in massive networks. However, in many domains, the…
A prominent tool in many problems involving metric spaces is a notion of randomized low-diameter decomposition. Loosely speaking, $\beta$-decomposition refers to a probability distribution over partitions of the metric into sets of low…
A $(\beta,\epsilon)$-hopset for a weighted undirected $n$-vertex graph $G=(V,E)$ is a set of edges, whose addition to the graph guarantees that every pair of vertices has a path between them that contains at most $\beta$ edges, whose length…
We present a framework for designing differentially private (DP) mechanisms for binary functions via a graph representation of datasets. Datasets are nodes in the graph and any two neighboring datasets are connected by an edge. The true…
We study the problem of continually releasing statistics of an evolving dataset under differential privacy. In the event-level setting, we show the first polynomial lower bounds on the additive error for insertions-only graph problems such…
All Colors Shortest Path problem defined on an undirected graph aims at finding a shortest, possibly non-simple, path where every color occurs at least once, assuming that each vertex in the graph is associated with a color known in…
We study a new framework for designing differentially private (DP) mechanisms via randomized graph colorings, called rainbow differential privacy. In this framework, datasets are nodes in a graph, and two neighboring datasets are connected…
We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$.…
In large networks, using the length of shortest paths as the distance measure has shortcomings. A well-studied shortcoming is that extending it to disconnected graphs and directed graphs is controversial. The second shortcoming is that a…
In this paper, we address the challenge of differential privacy in the context of graph cuts, specifically focusing on the multiway cut and the minimum $k$-cut. We introduce edge-differentially private algorithms that achieve nearly optimal…
Computing the core decomposition of a graph is a fundamental problem that has recently been studied in the differentially private setting, motivated by practical applications in data mining. In particular, Dhulipala et al. [FOCS 2022] gave…
Differential privacy is the de-facto privacy standard in data analysis. The classic model of differential privacy considers the data to be static. The dynamic setting, called differential privacy under continual observation, captures many…
A range counting problem is specified by a set $P$ of size $|P| = n$ of points in $\mathbb{R}^d$, an integer weight $x_p$ associated to each point $p \in P$, and a range space ${\cal R} \subseteq 2^{P}$. Given a query range $R \in {\cal…