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Given a graph $G$ and a set $Q$ of query nodes, we examine the Steiner Maximum-Connected Subgraph (SMCS) problem. The SMCS, or $G$ 's induced subgraph that contains $Q$ with the largest connectivity, can be useful for customer prediction, product promotion, and team assembling. Despite its importance, the SMCS problem has only been recently studied. Existing solutions evaluate the maximum SMCS, whose number of nodes is the largest among all the SMCSs of $Q$ . However, the maximum SMCS, which may contain a lot of nodes, can be difficult to interpret. In this paper, we investigate the minimal SMCS , which is the minimal subgraph of $G$ with the maximum connectivity containing $Q$ . The minimal SMCS contains much fewer nodes than its maximum counterpart, and is thus easier to be understood. However, the minimal SMCS can be costly to evaluate. We thus propose efficient Expand-Refine algorithms, as well as their approximate versions with accuracy guarantees. We further develop a cache-based processing model to improve the efficiency for an important case when $Q$ consists of a single node. Extensive experiments on large real and synthetic graph datasets validate the effectiveness and efficiency of our approaches. [ABSTRACT FROM PUBLISHER]

Existing studies on keyword search over relational databases usually find Steiner trees composed of connected database tuples as answers. They on-the-fly identify Steiner trees by discovering rich structural relationships between database tuples, and neglect the fact that such structural relationships can be precomputed and indexed. Recently, tuple units are proposed to improve search efficiency by indexing structural relationships, and existing methods identify a single tuple unit to answer keyword queries. However, in many cases, multiple tuple units should be integrated to answer a keyword query. Thus, these methods will involve false negatives. To address this problem, in this paper, we study how to integrate multiple related tuple units to effectively answer keyword queries. To achieve a high performance, we devise two novel indexes, single-keyword-based structure-aware index and keyword-pair-based structure-aware index, and incorporate structural relationships between different tuple units into the indexes. We use the indexes to efficiently identify the answers of integrated tuple units. We develop new ranking techniques and algorithms to progressively find the top-k answers. We have implemented our method in real database systems, and the experimental results show that our approach achieves high search efficiency and result quality, and outperforms state-of-the-art methods significantly. [ABSTRACT FROM PUBLISHER]