arXiv subjects

Roodabeh Safavi

Publications and source records attributed to Roodabeh Safavi.

4 recordsLinked to original sources

arXiv2026

Edit-Neighboring Data Streams and Privacy under Continual Observation

Differential privacy under Continual Observation (CO) quantifies the loss in privacy that occurs when outputs generated using a stream of sensitive input data are published in the online setting. In this paper, we consider a more stringent notion of privacy compared to prior work wherein an individual's participation may shift the entire stream by a time-step. We define a new notion of edit-neighboring streams that captures this scenario. Our findings are as follows. First, we prove that on a stream of length $T$, every additive-noise mechanism incurs error $\tildeΩ(\min\{T^{1/3}/\varepsilon^{2/3}, T\})$ when required to be $\varepsilon$-DP under CO for edit-neighboring streams. This includes state-of-the-art continual counters constructed via the factorization mechanism that in the standard neighboring setting incur only polylogarithmic additive error. Second, we construct the first mechanisms with polylogarithmic additive error for our more stringent notion of privacy. We show that we can recover the same additive error as in the standard notion of privacy albeit with worse constant coefficients for both arbitrary input streams and sparse streams. Third, we show that the notion of edit-neighboring streams inhabits a `sweet-spot' in terms of generality and additive error incurred. More precisely, we show that the even more general notion of prefix-sum neighboring streams---which arises naturally in reductions for problems under CO---must incur additive error scaling as $\tildeΩ(\min\{T^{1/3}/\varepsilon^{2/3}, T\})$ for any mechanism that is $\varepsilon$-DP under continual observation. Finally, we show empirically on synthetic data that when compared with prior work, our mechanism achieves a superior trade-off between the success probability of a simple distinguishing attack, and the additive error incurred by the respective mechanisms.

cs.DS↗

arXiv2026

Concurrent Composition for Differentially Private Continual Mechanisms

Many intended uses of differential privacy involve a $\textit{continual mechanism}$ that is set up to run continuously over a long period of time, making more statistical releases as either queries come in or the dataset is updated. In this paper, we give the first general treatment of privacy against $\textit{adaptive}$ adversaries for mechanisms that support dataset updates and a variety of queries, all arbitrarily interleaved. It also models a very general notion of neighboring, that includes both event-level and user-level privacy. We prove several $\textit{concurrent}$ composition theorems for continual mechanisms, which ensure privacy even when an adversary can interleave queries and dataset updates to the different composed mechanisms. Previous concurrent composition theorems for differential privacy were only for the case when the dataset is static, with no adaptive updates. Moreover, we also give the first interactive and continual generalizations of the "parallel composition theorem" for noninteractive differential privacy. Specifically, we show that the analogue of the noninteractive parallel composition theorem holds if either there are no adaptive dataset updates or each of the composed mechanisms satisfies pure differential privacy, but it fails to hold for composing approximately differentially private mechanisms with dataset updates. We then formalize a set of general conditions on a continual mechanism $M$ that runs multiple continual sub-mechanisms such that the privacy guarantees of $M$ follow directly using the above concurrent composition theorems on the sub-mechanisms, without further privacy loss. This enables us to give a simpler and more modular privacy analysis of a recent continual histogram mechanism of Henzinger, Sricharan, and Steiner. In the case of approximate DP, ours is the first proof showing that its privacy holds against adaptive adversaries.

cs.DS↗

arXiv2025

Counting Perfect Matchings In Dirac Hypergraphs

One of the foundational theorems of extremal graph theory is Dirac's theorem, which says that if an n-vertex graph G has minimum degree at least n/2, then G has a Hamilton cycle, and therefore a perfect matching (if n is even). Later work by Sárkozy, Selkow and Szemerédi showed that in fact Dirac graphs have many Hamilton cycles and perfect matchings, culminating in a result of Cuckler and Kahn that gives a precise description of the numbers of Hamilton cycles and perfect matchings in a Dirac graph G (in terms of an entropy-like parameter of G). In this paper we extend Cuckler and Kahn's result to perfect matchings in hypergraphs. For positive integers d < k, and for n divisible by k, let $m_{d}(k,n)$ be the minimum d-degree that ensures the existence of a perfect matching in an n-vertex k-uniform hypergraph. In general, it is an open question to determine (even asymptotically) the values of $m_{d}(k,n)$, but we are nonetheless able to prove an analogue of the Cuckler-Kahn theorem, showing that if an n-vertex k-uniform hypergraph G has minimum d-degree at least $(1+γ)m_{d}(k,n)$ (for any constant $γ>0$), then the number of perfect matchings in G is controlled by an entropy-like parameter of G. This strengthens cruder estimates arising from work of Kang-Kelly-Kühn-Osthus-Pfenninger and Pham-Sah-Sawhney-Simkin.

math.CO↗

arXiv2023

B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load

Uniquely represented data structures represent each logical state with a unique storage state. We study the problem of maintaining a dynamic set of $n$ keys from a totally ordered universe in this context. We introduce a two-layer data structure called $(α,\varepsilon)$-Randomized Block Search Tree (RBST) that is uniquely represented and suitable for external memory. Though RBSTs naturally generalize the well-known binary Treaps, several new ideas are needed to analyze the {\em expected} search, update, and storage, efficiency in terms of block-reads, block-writes, and blocks stored. We prove that searches have $O(\varepsilon^{-1} + \log_αn)$ block-reads, that $(α, \varepsilon)$-RBSTs have an asymptotic load-factor of at least $(1-\varepsilon)$ for every $\varepsilon \in (0,1/2]$, and that dynamic updates perform $O(\varepsilon^{-1} + \log_α(n)/α)$ block-writes, i.e. $O(1/\varepsilon)$ writes if $α=Ω(\frac{\log n}{\log \log n} )$. Thus $(α, \varepsilon)$-RBSTs provide improved search, storage-, and write-efficiency bounds in regard to the known, uniquely represented B-Treap [Golovin; ICALP'09].

cs.DS↗