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

1 対全ノードに対するs-t 信頼性の高速推定

s-t 信頼性は不確実グラフにおいて２ノード間の接続確率を評価する重要な指標のひとつである．s-t 信頼性の計算は♯P 完全であるため，近似解を計算する手法が提案されている．しかしながら，不確実グラフにおいてtop-k検索やクラスタリングなどの分析処理を実行するためには，1 対全ノードに対するs-t 信頼性計算を繰り返し実行する必要がある．この処理は，これまで提案されてきた近似的な計算手法を用いた場合でも，計算コストが膨大となり，大規模な不確実グラフを効率的に分析することが難しい．そこで本研究では，1 対全ノードに対する高速なs-t 信頼性推定手法を提案する．提案手法では幅優先探索とグラフサンプリングに基づくs-t 信頼性推定手法を統合する．これにより，少ない計算回数で高精度に1 対全ノードに対するs-t 信頼性を推定する．第12回データ工学と情報マネジメントに関するフォーラム (DEIM2020)日時：2020年3月2日～4日　オンライン開

Shortest paths and centrality in uncertain networks

Computing the shortest path between a pair of nodes is a fundamental graph primitive, which has critical applications in vehicle routing, finding functional pathways in biological networks, survivable network design, among many others. In this work, we study shortest-path queries over uncertain networks, i.e., graphs where every edge is associated with a probability of existence. We show that, for a given path, it is #P-hard to compute the probability of it being the shortest path, and we also derive other interesting properties highlighting the complexity of computing the Most Probable Shortest Paths (MPSPs). We thus devise sampling-based efficient algorithms, with end-to-end accuracy guarantees, to compute the MPSP. As a concrete application, we show how to compute a novel concept of betweenness centrality in an uncertain graph using MPSPs. Our thorough experimental results and rich real-world case studies on sensor networks and brain networks validate the effectiveness, efficiency, scalability, and usefulness of our solution