XML and other semi-structured data may have partially specified or missing schema information, motivating the use of a structural summary which can be automatically computed from the data. These summaries also serve as indices for evaluating the complex path expressions common to XML and semi-structured query languages. However, to answer all path queries accurately, summaries must encode information about long, seldom-queried paths, leading to increased size and complexity with little added value. We introduce the A(k)-indices, a family of approximate structural summaries. They are based on the concept of k-bisimilarity, in which nodes are grouped based on local structure, i.e., the incoming paths of length up to k. The parameter k thus smoothly varies the level of detail (and accuracy) of the A(k)-index. For small values of k, the size of the index is substantially reduced. While smaller, the A(k) index is approximate, and we describe techniques for efficiently extracting exact answers to regular path queries. Our experiments show that, for moderate values of k, path evaluation using the A(k)-index ranges from being very efficient for simple queries to competitive for most complex queries, while using significantly less space than comparable structures.

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The concept of support is central to data mining. While the definition of support in transaction databases is intuitive and simple, that is not the case in graph datasets and databases. Most mining algorithms require the support of a pattern to be no greater than that of its subpatterns, a property called anti-monotonicity, or admissibility. This paper examines the requirements for admissibility of a support measure. Support measures for mining graphs are usually based on the notion of an instance graph-a graph representing all the instances of the pattern in a database and their intersection properties. Necessary and sufficient conditions for support measure admissibility, based on operations on instance graphs, are developed and proved. The sufficient conditions are used to prove admissibility of one support measurethe size of the independent set in the instance graph. Conversely, the necessary conditions are used to quickly show that some other support measures, such as weighted count of instances, are not admissible.

Virtual communities become more and more heterogeneous as their scale increases. This implies that, rather than being a single, homogeneous community, they become a collection of knots (or sub-communities) of users. For the computation of a member's reputation to be useful, the system must therefore identify the community knot to which this member belongs and to interpret its reputation data correctly. Unfortunately, to the best of our knowledge existing trust-based reputation models treat a community as a single entity and do not explicitly address this issue. In this paper, we introduce the knot-aware trust-based reputation model for large-scale virtual communities. We define a knot as a group of community members having overall "strong" trust relations between them. Different knots typically represent different view points and preferences. It is therefore plausible that the reputation of the same member in different knots assign may differ significantly. Using our knot-aware approach, we can deal with heterogeneous communities where a member's reputation may be distributed in a multi modal manner. As we show, an interesting and beneficial feature of our knot-aware model is that it naturally prevents malicious attempts to bias community members' reputation.