Flajolet-Martin Sketch Research Articles

An Effective and Differentially Private Protocol for Secure Distributed Cardinality Estimation

Counting the number of distinct elements distributed over multiple data holders is a fundamental problem with many real-world applications ranging from crowd counting to network monitoring. Although a number of space and computationally efficient sketch methods (e.g., the Flajolet-Martin sketch and the HyperLogLog sketch) for cardinality estimation have been proposed to solve the above problem, these sketch methods are insecure when considering privacy concerns related to the use of each data holder's personal dataset. Despite a recently proposed protocol that successfully implements the well-known Flajolet-Martin (FM) sketch on a secret-sharing based multiparty computation (MPC) framework for solving the problem of private distributed cardinality estimation (PDCE), we observe that this MPC-FM protocol is not differentially private. In addition, the MPC-FM protocol is computationally expensive, which limits its applications to data holders with limited computation resources. To address the above issues, in this paper we propose a novel protocol DP-DICE, which is computationally efficient and differentially private for solving the problem of PDCE. Experimental results show that our DP-DICE achieves orders of magnitude speedup and reduces the estimation error by several times in comparison with state-of-the-arts under the same security requirements.

Differentially Private Vertical Federated Clustering

In many applications, multiple parties have private data regarding the same set of users but on disjoint sets of attributes, and a server wants to leverage the data to train a model. To enable model learning while protecting the privacy of the data subjects, we need vertical federated learning (VFL) techniques, where the data parties share only information for training the model, instead of the private data. However, it is challenging to ensure that the shared information maintains privacy while learning accurate models. To the best of our knowledge, the algorithm proposed in this paper is the first practical solution for differentially private vertical federated k -means clustering, where the server can obtain a set of global centers with a provable differential privacy guarantee. Our algorithm assumes an untrusted central server that aggregates differentially private local centers and membership encodings from local data parties. It builds a weighted grid as the synopsis of the global dataset based on the received information. Final centers are generated by running any k -means algorithm on the weighted grid. Our approach for grid weight estimation uses a novel, light-weight, and differentially private set intersection cardinality estimation algorithm based on the Flajolet-Martin sketch. To improve the estimation accuracy in the setting with more than two data parties, we further propose a refined version of the weights estimation algorithm and a parameter tuning strategy to reduce the final k -means loss to be close to that in the central private setting. We provide theoretical utility analysis and experimental evaluation results for the cluster centers computed by our algorithm and show that our approach performs better both theoretically and empirically than the two baselines based on existing techniques.

Fast and Error-Adaptive Influence Maximization Based on Count-Distinct Sketches

Influence maximization (IM) is the problem of finding a seed vertex set that maximizes the expected number of vertices influenced under a given diffusion model. Due to the NP-Hardness of finding an optimal seed set, approximation algorithms are frequently used for IM. In this work, we describe a fast, error-adaptive approach that leverages Count-Distinct sketches and hash-based fused sampling. To estimate the number of influenced vertices throughout a diffusion, we use per-vertex Flajolet-Martin sketches where each sketch corresponds to a sampled subgraph. To efficiently simulate the diffusions, the reach-set cardinalities of a single vertex are stored in memory in a consecutive fashion. This allows the proposed algorithm to estimate the number of influenced vertices in a single step for simulations at once. For a faster IM kernel, we rebuild the sketches in parallel only after observing estimation errors above a given threshold. Our experimental results show that the proposed algorithm yields high-quality seed sets while being up to 119x faster than a state-of-the-art approximation algorithm. In addition, it is up to 62x faster than a sketch-based approach while producing seed sets with 3%-12% better influence scores

PPDC: A Privacy-Preserving Distinct Counting Scheme for Mobile Sensing

Mobile sensing mines group information through sensing and aggregating users’ data. Among major mobile sensing applications, the distinct counting problem aiming to find the number of distinct elements in a data stream with repeated elements, is extremely important for avoiding waste of resources. Besides, the privacy protection of users is also a critical issue for aggregation security. However, it is a challenge to meet these two requirements simultaneously since normal privacy-preserving methods would have negative influence on the accuracy and efficiency of distinct counting. In this paper, we propose a Privacy-Preserving Distinct Counting scheme (PPDC) for mobile sensing. Through integrating the basic idea of homomorphic encryption into Flajolet-Martin (FM) sketch, PPDC allows an aggregator to conduct distinct counting over large-scale datasets without disrupting privacy of users. Moreover, PPDC supports various forms of sensing data, including camera images, location data, etc. PPDC expands each bit of the hashing values of users’ original data, FM sketch is thus enhanced for encryption to protect users’ privacy. We prove the security of PPDC under known-plaintext model. The theoretic and experimental results show that PPDC achieves high counting accuracy and practical efficiency with scalability over large-scale data sets.

Approximating Private Set Union/Intersection Cardinality With Logarithmic Complexity

The computation of private set union/intersection cardinality (PSU-CA/PSI-CA) is one of the most intensively studied problems in privacy preserving data mining (PPDM). However, the existing protocols are computationally too expensive to be employed in real-world PPDM applications. In response, we propose efficient approximate protocols, whose accuracy can be tuned according to application requirements. We first propose a two-party PSU-CA protocol based on Flajolet-Martin sketches. The protocol has logarithmic computational/communication complexity and relies mostly on symmetric key operations. Thus, it is much more efficient and scalable than existing protocols. In addition, our protocol can hide its output. This feature is necessary in PPDM applications, since the union cardinality is often an intermediate result that must not be disclosed. We then propose a two-party PSI-CA protocol, which is derived from the PSU-CA protocol with virtually no cost. Both our two-party protocols can be easily extended to the multiparty setting. We also design an efficient masking scheme for $(^{1}_{n}){-}OT$ . The scheme is used in optimizing the two-party protocols and is of independent interest, since it can speed up $(^{1}_{n}){-}OT$ significantly when $n$ is large. Finally, we show through experiments the effectiveness and efficiency of our protocols.

Building, sharing and exploiting spatio- temporal aggregates in vehicular networks

This article focuses on data aggregation in vehicular ad hoc networks (VANETs). In such networks, data produced by sensors or crowdsourcers are exchanged between vehicles in order to warn or inform drivers when an event occurs (e.g., an accident, a traffic congestion, a parking space released, a vehicle with non-functioning brake lights, etc.). In the following, we propose to generate spatio-temporal aggregates containing these data in order to keep a summary of past events. We therefore use Flajolet-Martin sketches. Our goal is then to exploit these aggregates to better assist the drivers. These aggregates may indeed produce additional knowledge that may be useful when no event has been recently transmitted by surrounding vehicles or when some knowledge about the global demand may improve the decision that need to be taken at the vehicle level. To prove the effectiveness of our approach, an extensive experimental evaluation has been performed considering vehicles looking for an available parking space, that proves the interest of our proposal. The experimentations indeed show that the use of our aggregation structure significantly reduces the time needed to actually find a parking space. It also increases the percentage of vehicles finding such a resource in a bounded time in congested situations.

Ranking weighted clustering coefficient in large dynamic graphs

Efficiently searching top-k representative vertices is crucial for understanding the structure of large dynamic graphs. Recent studies show that communities formed by a vertex with high local clustering coefficient and its neighbours can achieve enhanced information propagation speed as well as disease transmission speed. However, local clustering coefficient, which measures the cliquishness of a vertex in its local neighbourhood, prefers vertices with small degrees. To remedy this issue, in this paper we propose a new ranking measure, weighted clustering coefficient (WCC) of vertices, by integrating both local clustering coefficient and degree. WCC not only inherits the properties of local clustering coefficient but also approximately measures the density (i.e., average degree) of its neighbourhood subgraph. Thus, vertices with higher WCC are more likely to be representative. We study efficiently computing and monitoring top-k representative vertices based on WCC over large dynamic graphs. To reduce the search space, we propose a series of heuristic upper bounds for WCC to prune a large portion of disqualifying vertices from the search space. We also develop an approximation algorithm by utilizing Flajolet-Martin sketch to trade acceptable accuracy for enhanced efficiency. An efficient incremental algorithm dealing with frequent updates in dynamic graphs is explored as well. Extensive experimental results on a variety of real-life graph datasets demonstrate the efficiency and effectiveness of our approaches.

A New Sketch Method for Measuring Host Connection Degree Distribution

The host connection degree distribution (HCDD) is an important metric for network security monitoring. However, it is difficult to accurately obtain the HCDD in real time for high-speed links with a massive amount of traffic data. In this paper, we propose a new sketch method to build a probabilistic traffic summary of a host's flows using a uniform Flajolet-Martin sketch combined with a small bitmap. To study its performance in comparison with previous sampling and sketch methods, we present a general model that encompasses all these methods. With this model, we compute the Cramer-Rao lower bounds and the variances of HCDD estimations. The theoretic analysis and numerical experimental results show that our sketch method is six times more accurate than state-of-the-art methods with the same memory usage.

Building, Sharing and Exploiting Spatio-Temporal Aggregates in Vehicular Networks

This article focuses on data aggregation in vehicular ad hoc networks (VANETs). In such networks, data produced by sensors or crowdsourcers are exchanged between vehicles in order to warn or inform drivers when an event occurs (e.g., an accident, a traffic congestion, a parking space released, a vehicle with non-functioning brake lights, etc.). In the following, we propose to generate spatio-temporal aggregates containing these data in order to keep a summary of past events. We therefore use Flajolet-Martin sketches. Our goal is then to exploit these aggregates to better assist the drivers. These aggregates may indeed produce additional knowledge that may be useful when no event has been recently transmitted by surrounding vehicles or when some knowledge about the global demand may improve the decision that need to be taken at the vehicle level. To prove the effectiveness of our approach, an extensive experimental evaluation has been performed considering vehicles looking for an available parking space, that proves the interest of our proposal. The experimentations indeed show that the use of our aggregation structure significantly reduces the time needed to actually find a parking space. It also increases the percentage of vehicles finding such a resource in a bounded time in congested situations.

A Secure and Efficient Data Aggregation Framework in Vehicular Sensing Networks

Vehicular ad hoc networks support a wide range of promising applications including vehicular sensing networks, which enable vehicles to cooperatively collect and transmit the aggregated traffic data for the purpose of traffic monitoring. The reported literatures mainly focus on how to achieve the data aggregation in dynamic vehicular environment, while the security issue especially on the authenticity and integrity of aggregation results receives less attention. In this study, we introduce a basic aggregation scheme which could aggregate the data and the message authentication codes by using syntactic aggregation and cryptographic aggregation. To tolerate duplicate messages and further improve the aggregation performance, we introduce a secure probabilistic data aggregation scheme based on Flajolet-Martin sketch and sketch proof technique. We also discuss the tradeoff between the bandwidth efficiency and the estimation accuracy. Extensive simulations and analysis demonstrate the efficiency and effectiveness of the proposed scheme.

Summarizing sensors data in vehicularad hocnetworks

This article focuses on data aggregation in vehicular ad hoc networks. In such networks, sensor data are usually produced and exchanged between vehicles in order to warn or inform the drivers when an event is detected (e.g. , accident, emergency braking, parking space released, vehicle with non-functioning brake lights, etc. ). In the following, we present a solution to aggregate and store these data in order to have a history of past events. We therefore use Flajolet-Martin sketches. Our goal is to generate additional knowledge to assist drivers by providing them useful information even if no event is transmitted by vehicles in the vicinity.

A probabilistic method for cooperative hierarchical aggregation of data in VANETs

We propose an algorithm for the hierarchical aggregation of observations in dissemination-based, distributed traffic information systems. Instead of transmitting observed parameters directly, we propose soft-state sketches—an extension of Flajolet–Martin sketches—as a probabilistic approximation. This data representation is duplicate insensitive, a trait that overcomes two central problems of existing aggregation schemes for VANET applications. First, when multiple aggregates of observations for the same area are available, it is possible to combine them into an aggregate containing all information from the original aggregates. This is fundamentally different from existing approaches where typically one of the aggregates is selected for further use while the rest is discarded. Second, any observation or aggregate can be included into higher-level aggregates, regardless if it has already been previously—directly or indirectly—added. Those characteristics result in a very flexible aggregate construction and a high quality of the aggregates. We demonstrate these traits of our approach by a simulation study.