Distributed Data Summarization in Well-Connected Networks

We study distributed algorithms for some fundamental problems in data summarization. Given a communication graph G of n nodes each of which may hold a value initially, we focus on computing sum_{i=1}^N g(f_i), where f_i is the number of occurrences of value i and g is some fixed function. This includes important statistics such as the number of distinct elements, frequency moments, and the empirical entropy of the data. In the CONGEST~ model, a simple adaptation from streaming lower bounds shows that it requires Omega~(D+ n) rounds, where D is the diameter of the graph, to compute some of these statistics exactly. However, these lower bounds do not hold for graphs that are well-connected. We give an algorithm that computes sum_{i=1}^{N} g(f_i) exactly in {tau_{G}} * 2^{O(sqrt{log n})} rounds where {tau_{G}} is the mixing time of G. This also has applications in computing the top k most frequent elements. We demonstrate that there is a high similarity between the GOSSIP~ model and the CONGEST~ model in well-connected graphs. In particular, we show that each round of the GOSSIP~ model can be simulated almost perfectly in O~({tau_{G}}) rounds of the CONGEST~ model. To this end, we develop a new algorithm for the GOSSIP~ model that 1 +/- epsilon approximates the p-th frequency moment F_p = sum_{i=1}^N f_i^p in O~(epsilon^{-2} n^{1-k/p}) roundsfor p >= 2, when the number of distinct elements F_0 is at most O(n^{1/(k-1)}). This result can be translated back to the CONGEST~ model with a factor O~({tau_{G}}) blow-up in the number of rounds

Privacy-enhancing Aggregation of Internet of Things Data via Sensors Grouping

Big data collection practices using Internet of Things (IoT) pervasive technologies are often privacy-intrusive and result in surveillance, profiling, and discriminatory actions over citizens that in turn undermine the participation of citizens to the development of sustainable smart cities. Nevertheless, real-time data analytics and aggregate information from IoT devices open up tremendous opportunities for managing smart city infrastructures. The privacy-enhancing aggregation of distributed sensor data, such as residential energy consumption or traffic information, is the research focus of this paper. Citizens have the option to choose their privacy level by reducing the quality of the shared data at a cost of a lower accuracy in data analytics services. A baseline scenario is considered in which IoT sensor data are shared directly with an untrustworthy central aggregator. A grouping mechanism is introduced that improves privacy by sharing data aggregated first at a group level compared as opposed to sharing data directly to the central aggregator. Group-level aggregation obfuscates sensor data of individuals, in a similar fashion as differential privacy and homomorphic encryption schemes, thus inference of privacy-sensitive information from single sensors becomes computationally harder compared to the baseline scenario. The proposed system is evaluated using real-world data from two smart city pilot projects. Privacy under grouping increases, while preserving the accuracy of the baseline scenario. Intra-group influences of privacy by one group member on the other ones are measured and fairness on privacy is found to be maximized between group members with similar privacy choices. Several grouping strategies are compared. Grouping by proximity of privacy choices provides the highest privacy gains. The implications of the strategy on the design of incentives mechanisms are discussed

Graph Summarization

The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is graph summarization. It denotes a series of application-specific algorithms designed to transform graphs into more compact representations while preserving structural patterns, query answers, or specific property distributions. As this problem is common to several areas studying graph topologies, different approaches, such as clustering, compression, sampling, or influence detection, have been proposed, primarily based on statistical and optimization methods. The focus of our chapter is to pinpoint the main graph summarization methods, but especially to focus on the most recent approaches and novel research trends on this topic, not yet covered by previous surveys.Comment: To appear in the Encyclopedia of Big Data Technologie