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 performance for these problems. Motivated by multiway cut, we propose the shifting mechanism, a general framework for private combinatorial optimization problems. This framework allows us to develop an efficient private algorithm with a multiplicative approximation ratio that matches the state-of-the-art non-private algorithm, improving over previous private algorithms that have provably worse multiplicative loss. We then provide a tight information-theoretic lower bound on the additive error, demonstrating that for constant \(k\), our algorithm is optimal in terms of the privacy cost. The shifting mechanism also allows us to design private algorithm for the multicut and max-cut problems, with runtimes determined by the best nonprivate algorithms for these tasks. For the minimum \(k\)-cut problem we use a different approach, combining the exponential mechanism with bounds on the number of approximate \(k\)-cuts to get the first private algorithm with optimal additive error of \(O(k \log n)\) (for a fixed privacy parameter). We also establish an information-theoretic lower bound that matches this additive error. Furthermore, we provide an efficient private algorithm even for non-constant \(k\), including a polynomial-time 2-approximation with an additive error of \(\tilde O(k^{1.5})\).

In this paper, we give an almost linear time and space algorithms to sample from an exponential mechanism with an $\ell_1$-score function defined over an exponentially large non-convex set. As a direct result, on input an $n$ vertex $m$ edges graph $G$, we present the first $\widetilde{O}(m)$ time and $O(m)$ space algorithms for differentially privately outputting an $n$ vertex $O(m)$ edges synthetic graph that approximates all the cuts and the spectrum of $G$. These are the first private algorithms for releasing synthetic graphs that nearly match this task’s time and space complexity in the non-private setting while achieving the same (or better) utility as the previous works in the more practical sparse regime. Additionally, our algorithms can be extended to private graph analysis under continual observation.

We show that spin systems with bounded degrees and coupling independence admit fully polynomial time approximation schemes (FPTAS). We design a new recursive deterministic counting algorithm to achieve this. As applications, we give the first FPTASes for q-colourings on graphs of bounded maximum degree $\Delta \geq 3$, when $q \geq\left(11 / 6-\varepsilon_{0}\right) \Delta$ for some small $\varepsilon_{0} \approx 10^{-5}$, or when $\Delta \geq 125$ and $q \geq 1.809 \Delta$, and on graphs with sufficiently large (but constant) girth, when $q \geq \Delta+3$. These bounds match the current best randomised approximate counting algorithms by Chen, Delcourt, Moitra, Perarnau, and Postle (2019), Carlson and Vigoda (2024), and Chen, Liu, Mani, and Moitra (2023), respectively.

We study the problem of approximating all-pair distances in a weighted undirected graph with differential privacy, introduced by Sealfon [Sea16]. Given a publicly known undirected graph, we treat the weights of edges as sensitive information, and two graphs are neighbors if their edge weights differ in one edge by at most one. We obtain efficient algorithms with significantly improved bounds on a broad class of graphs which we refer to as *recursively separable*. In particular, for any $n$-vertex $K_h$-minor-free graph, our algorithm achieve an additive error of $ \widetilde{O}(h(nW)^{1/3} ) $, where $ W $ represents the maximum edge weight; For grid graphs, the same algorithmic scheme achieve additive error of $ \widetilde{O}(n^{1/4}\sqrt{W}) $. Our approach can be seen as a generalization of the celebrated binary tree mechanism for range queries, as releasing range queries is equivalent to computing all-pair distances on a path graph. In essence, our approach is based on generalizing the binary tree mechanism to graphs that are *recursively separable*.

We give a Õ(n) time almost uniform sampler for independent sets of a matroid, whose ground set has n elements and is given by an independence oracle. As a consequence, one can sample connected spanning subgraphs of a given graph G = (V,E) in Õ(|E|) time, whereas the previous best algorithm takes O(|E||V|) time. This improvement, in turn, leads to a faster running time on estimating all-terminal network reliability. Furthermore, we generalise this near-linear time sampler to the random cluster model with q ≤ 1.

We propose an efficient ɛ-differentially private algorithm, that given a simple weighted n-vertex, m-edge graph G with a maximum unweighted degree Δ(G) ≤ n - 1, outputs a synthetic graph which approximates the spectrum with Õ(min{Δ(G), √n}) bound on the purely additive error. To the best of our knowledge, this is the first ɛ-differentially private algorithm with a non-trivial additive error for approximating the spectrum of the graph. One of our subroutines also precisely simulates the exponential mechanism over a non-convex set, which could be of independent interest given the recent interest in sampling from a log-concave distribution defined over a convex set. As a direct application of our result, we give the first non-trivial bound on approximating all-pairs effective resistances by a synthetic graph, which also implies approximating hitting/commute time and cover time of random walks on the graph. Given the significance of effective resistance in understanding the statistical properties of a graph, we believe our result would have further implications.

Decentralized learning involves training machine learning models over remote mobile devices, edge servers, or cloud servers while keeping data localized. Even though many studies have shown the feasibility of preserving privacy, enhancing training performance or introducing Byzantine resilience, but none of them simultaneously considers all of them. Therefore we face the following problem:how can we efficiently coordinate the decentralized learning process while simultaneously maintaining learning security and data privacy for the entire system?To address this issue, in this paper we propose SPDL, a blockchain-secured and privacy-preserving decentralized learning system. SPDL integrates blockchain, Byzantine Fault-Tolerant (BFT) consensus, BFT Gradients Aggregation Rule (GAR), and differential privacy seamlessly into one system, ensuring efficient machine learning while maintaining data privacy, Byzantine fault tolerance, transparency, and traceability. To validate our approach, we provide rigorous analysis on convergence and regret in the presence of Byzantine nodes. We also build a SPDL prototype and conduct extensive experiments to demonstrate that SPDL is effective and efficient with strong security and privacy guarantees.

Training machine learning models in a decentralized way has attracted tremendous attention on intelligent Internet of Vehicles (IIoV). However, it is highly dynamic and asymmetric for the connections between vehicles in IIoV due to the mobility of vehicles and the complex communication environment, which poses great challenges on designing efficient distributed learning algorithms. To address this problem, we focus on the basic stochastic gradient descent (SGD) algorithm and propose a decentralized parallel SGD algorithm (DPSGD-WB) for the complex IIoV. The algorithm is based on weight-balancing to overcome the difficulty caused by the dynamic and asymmetric connectivity in IIoV. With rigorous analysis, we show that DPSGD-WB converges on the optimal rate of$O(1/\sqrt {Kn})$, where$n$is the number of vehicle terminals and$K$is the number of iterations. To the best of our knowledge, our proposed algorithm is the first known decentralized parallel SGD algorithm that can be implemented in asymmetric and dynamic intelligent IoV systems. Finally, extensive experiments demonstrate the efficacy of our algorithm.

This paper studies the privacy-preserving adaptive ranking problem for multi-armed-bandit crowdsourcing, where according to the crowdsourced data, the arms are required to be ranked with a tunable granularity by the untrustworthy third-party platform. Any online worker can provide its data by arm pulls but requires its privacy preserved, which will increase the ranking cost greatly. To improve the quality of the ranking service, we propose a Privacy- Preserving Adaptive Ranking algorithm called PPAR, which can solve the problem with a high probability while differential privacy can be ensured. The total cost of the proposed algorithm is ${\mathcal{O}}(K\ln K)$, which is near optimal compared with the trivial lower bound Ω(K), where K is the number of arms. Our proposed algorithm can also be used to solve the well-studied fully ranking problem and the best arm identification problem, by proper setting the granularity parameter. For the fully ranking problem, PPAR attains the same order of computation complexity with the best-known results without privacy preservation. The efficacy of our algorithm is also verified by extensive experiments on public datasets.

Decentralized machine learning has been playing an essential role in improving training efficiency. It has been applied in many real‐world scenarios, such as edge computing and IoT. However, in fact, networks are dynamic, and there is a risk of information leaking during the communication process. To address this problem, we propose a decentralized parallel stochastic gradient descent algorithm (D‐(DP)2SGD) with differential privacy in dynamic networks. With rigorous analysis, we show that D‐(DP)2SGD converges with a rate of while satisfying ε‐DP, which achieves almost the same convergence rate as previous works without privacy concern. To the best of our knowledge, our algorithm is the first known decentralized parallel SGD algorithm that can implement in dynamic networks and take privacy‐preserving into consideration.