We study the problem of preprocessing a large graph so that point-to-point shortest-path queries can be answered very fast. Computing shortest paths is a well studied problem, but exact algorithms do not scale to huge graphs encountered on the web, social networks, and other applications.In this paper we focus on approximate methods for distance estimation, in particular using landmark-based distance indexing. This approach involves selecting a subset of nodes as landmarks and computing (offline) the distances from each node in the graph to those landmarks. At runtime, when the distance between a pair of nodes is needed, we can estimate it quickly by combining the precomputed distances of the two nodes to the landmarks.We prove that selecting the optimal set of landmarks is an NP-hard problem, and thus heuristic solutions need to be employed. Given a budget of memory for the index, which translates directly into a budget of landmarks, different landmark selection strategies can yield dramatically different results in terms of accuracy. A number of simple methods that scale well to large graphs are therefore developed and experimentally compared. The simplest methods choose central nodes of the graph, while the more elaborate ones select central nodes that are also far away from one another. The efficiency of the suggested techniques is tested experimentally using five different real world graphs with millions of edges; for a given accuracy, they require as much as 250 times less space than the current approach in the literature which considers selecting landmarks at random.Finally, we study applications of our method in two problems arising naturally in large-scale networks, namely, social search and community detection.

Complex networks, such as biological, social, and communication networks, often entail uncertainty, and thus, can be modeled as probabilistic graphs. Similar to the problem of similarity search in standard graphs, a fundamental problem for probabilistic graphs is to efficiently answer k-nearest neighbor queries (k-NN), which is the problem of computing the k closest nodes to some specific node.In this paper we introduce a framework for processing k-NN queries in probabilistic graphs. We propose novel distance functions that extend well-known graph concepts, such as shortest paths. In order to compute them in probabilistic graphs, we design algorithms based on sampling. During k-NN query processing we efficiently prune the search space using novel techniques.Our experiments indicate that our distance functions outperform previously used alternatives in identifying true neighbors in real-world biological data. We also demonstrate that our algorithms scale for graphs with tens of millions of edges.

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Large-scale data analysis lies in the core of modern enterprises and scientific research. With the emergence of cloud computing, the use of an analytical query processing infrastructure can be directly associated with monetary cost. MapReduce has been a popular framework in the context of cloud computing, designed to serve long-running queries (jobs) which can be processed in batch mode. Taking into account that different jobs often perform similar work, there are many opportunities for sharing. In principle, sharing similar work reduces the overall amount of work, which can lead to reducing monetary charges for utilizing the processing infrastructure. In this article we present a sharing framework tailored to MapReduce, namely, <tt>MRShare</tt>. Our framework, <tt>MRShare</tt>, transforms a batch of queries into a new batch that will be executed more efficiently, by merging jobs into groups and evaluating each group as a single query. Based on our cost model for MapReduce, we define an optimization problem and we provide a solution that derives the optimal grouping of queries. Given the query grouping, we merge jobs appropriately and submit them to MapReduce for processing. A key property of <tt>MRShare</tt> is that it is independent of the MapReduce implementation. Experiments with our prototype, built on top of Hadoop, demonstrate the overall effectiveness of our approach. <tt>MRShare</tt> is primarily designed for handling I/O-intensive queries. However, with the development of high-level languages operating on top of MapReduce, user queries executed in this model become more complex and CPU intensive. Commonly, executed queries can be modeled as evaluating pipelines of CPU-expensive filters over the input stream. Examples of such filters include, but are not limited to, index probes, or certain types of joins. In this article we adapt some of the standard techniques for filter ordering used in relational and stream databases, propose their extensions, and implement them through <tt>MRAdaptiveFilter</tt>, an extension of <tt>MRShare</tt> for expensive filter ordering tailored to MapReduce, which allows one to handle both single- and batch-query execution modes. We present an experimental evaluation that demonstrates additional benefits of <tt>MRAdaptiveFilter</tt>, when executing CPU-intensive queries in <tt>MRShare</tt>.

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