In 2013, AmazonWeb Services revolutionized the data warehousing industry by launching Amazon Redshift, the first fully-managed, petabyte-scale, enterprise-grade cloud data warehouse. Amazon Redshift made it simple and cost-effective to efficiently analyze large volumes of data using existing business intelligence tools. This cloud service was a significant leap from the traditional on-premise data warehousing solutions, which were expensive, not elastic, and required significant expertise to tune and operate. Customers embraced Amazon Redshift and it became the fastest growing service in AWS. Today, tens of thousands of customers use Redshift in AWS's global infrastructure to process exabytes of data daily.

Uncertain graphs are prevalent in several applications including communications systems, biological databases and social networks. The ever increasing size of the underlying data renders both graph storage and query processing extremely expensive. Sparsification has often been used to reduce the size of deterministic graphs by maintaining only the important edges. However, adaptation of deterministic sparsification methods fails in the uncertain setting. To overcome this problem, we introduce the first sparsification techniques aimed explicitly at uncertain graphs. The proposed methods reduce the number of edges and redistribute their probabilities in order to decrease the graph size, while preserving its underlying structure. The resulting graph can be used to efficiently and accurately approximate any query and mining tasks on the original graph, including clustering coefficient, page rank, reliability and shortest path distance.

Uncertain graphs are prevalent in several applications including communications systems, biological databases, and social networks. The ever increasing size of the underlying data renders both graph storage and query processing extremely expensive. Sparsification has often been used to reduce the size of deterministic graphs by maintaining only the important edges. However, adaptation of deterministic sparsification methods fails in the uncertain setting. To overcome this problem, we introduce the first sparsification techniques aimed explicitly at uncertain graphs. The proposed methods reduce the number of edges and redistribute their probabilities in order to decrease the graph size, while preserving its underlying structure. The resulting graph can be used to efficiently and accurately approximate any query and mining tasks on the original graph. An extensive experimental evaluation with real and synthetic datasets illustrates the effectiveness of our techniques on several common graph tasks, including clustering coefficient, page rank, reliability, and shortest path distance.

Data in several applications can be represented as an uncertain graph whose edges are labeled with a probability of existence. Exact query processing on uncertain graphs is prohibitive for most applications, as it involves evaluation over an exponential number of instantiations. Thus, typical approaches employ Monte-Carlo sampling, which (i) draws a number of possible graphs (samples), (ii) evaluates the query on each of them, and (iii) aggregates the individual answers to generate the final result. However, this approach can also be extremely time consuming for large uncertain graphs commonly found in practice. To facilitate efficiency, we study the problem of extracting a single representative instance from an uncertain graph. Conventional processing techniques can then be applied on this representative to closely approximate the result on the original graph. In order to maintain data utility, the representative instance should preserve structural characteristics of the uncertain graph. We start with representatives that capture the expected vertex degrees, as this is a fundamental property of the graph topology. We then generalize the notion of vertex degree to the concept of n -clique cardinality, that is, the number of cliques of size n that contain a vertex. For the first problem, we propose two methods: Average Degree Rewiring (ADR), which is based on random edge rewiring, and Approximate B-Matching (ABM), which applies graph matching techniques. For the second problem, we develop a greedy approach and a game-theoretic framework. We experimentally demonstrate, with real uncertain graphs, that indeed the representative instances can be used to answer, efficiently and accurately, queries based on several metrics such as shortest path distance, clustering coefficient, and betweenness centrality.

Data in several applications can be represented as an uncertain graph, whose edges are labeled with a probability of existence. Exact query processing on uncertain graphs is prohibitive for most applications, as it involves evaluation over an exponential number of instantiations. Even approximate processing based on sampling is usually extremely expensive since it requires a vast number of samples to achieve reasonable quality guarantees. To overcome these problems, we propose algorithms for creating deterministic representative instances of uncertain graphs that maintain the underlying graph properties. Specifically, our algorithms aim at preserving the expected vertex degrees because they capture well the graph topology. Conventional processing techniques can then be applied on these instances to closely approximate the result on the uncertain graph. We experimentally demonstrate, with real and synthetic uncertain graphs, that indeed the representative instances can be used to answer, efficiently and accurately, queries based on several properties such as shortest path distance, clustering coefficient and betweenness centrality.