Set similarity joins compute all pairs of similar sets from two collections of sets. We conduct extensive experiments on seven state-of-the-art algorithms for set similarity joins. These algorithms adopt a filter-verification approach. Our analysis shows that verification has not received enough attention in previous works. In practice, efficient verification inspects only a small, constant number of set elements and is faster than some of the more sophisticated filter techniques. Although we can identify three winners, we find that most algorithms show very similar performance. The key technique is the prefix filter, and AllPairs, the first algorithm adopting this techniques is still a relevant competitor. We repeat experiments from previous work and discuss diverging results. All our claims are supported by a detailed analysis of the factors that determine the overall runtime.

We consider the classical tree edit distance between ordered labelled trees, which is defined as the minimum-cost sequence of node edit operations that transform one tree into another. The state-of-the-art solutions for the tree edit distance are not satisfactory. The main competitors in the field either have optimal worst-case complexity but the worst case happens frequently, or they are very efficient for some tree shapes but degenerate for others. This leads to unpredictable and often infeasible runtimes. There is no obvious way to choose between the algorithms. In this article we present RTED, a robust tree edit distance algorithm. The asymptotic complexity of our algorithm is smaller than or equal to the complexity of the best competitors for any input instance, that is, our algorithm is both efficient and worst-case optimal. This is achieved by computing a dynamic decomposition strategy that depends on the input trees. RTED is shown optimal among all algorithms that use LRH ( left-right-heavy ) strategies, which include RTED and the fastest tree edit distance algorithms presented in literature. In our experiments on synthetic and real-world data we empirically evaluate our solution and compare it to the state-of-the-art.

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When integrating data from autonomous sources, exact matches of data items that represent the same real-world object often fail due to a lack of common keys. Yet in many cases structural information is available and can be used to match such data. Typically the matching must be approximate since the representations in the sources differ.We propose pq-grams to approximately match hierarchical data from autonomous sources and define the pq-gram distance between ordered labeled trees as an effective and efficient approximation of the fanout weighted tree edit distance. We prove that the pq-gram distance is a lower bound of the fanout weighted tree edit distance and give a normalization of the pq-gram distance for which the triangle inequality holds. Experiments on synthetic and real-world data (residential addresses and XML) confirm the scalability of our approach and show the effectiveness of pq-grams. ACM Reference Format:Augsten, N., Böhlen, M., and Gamper, J. 2010. The pq-gram distance between ordered labeled trees.

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We consider the Top-k Approximate Subtree Matching (TASM) problem: finding the k best matches of a small query tree, e.g., a DBLP article with 15 nodes, in a large document tree, e.g., DBLP with 26M nodes, using the canonical tree edit distance as a similarity measure between subtrees. Evaluating the tree edit distance for large XML trees is difficult: the best known algorithms have cubic runtime and quadratic space complexity, and, thus, do not scale. Our solution is TASMpostorder, a memory-efficient and scalable TASM algorithm. We prove an upper-bound for the maximum subtree size for which the tree edit distance needs to be evaluated. The upper bound depends on the query and is independent of the document size and structure. A core problem is to efficiently prune subtrees that are above this size threshold. We develop an algorithm based on the prefix ring buffer that allows us to prune all subtrees above the threshold in a single postorder scan of the document. The size of the prefix ring buffer is linear in the threshold. As a result, the space complexity of TASM-postorder depends only on k and the query size, and the runtime of TASM-postorder is linear in the size of the document. Our experimental evaluation on large synthetic and real XML documents confirms our analytic results.

Synthesis Lectures on Data Management is edited by Tamer Özsu of the University of Waterloo. e series publishes 50-to 125 page publications on topics pertaining to data management. e scope will largely follow the purview of premier information and computer science conferences, such as ACM SIGMOD, VLDB, ICDE, PODS, ICDT, and ACM KDD. Potential topics include, but not are limited to: query languages, database system architectures, transaction management, data warehousing, XML and databases, data stream systems, wide scale data distribution, multimedia data management, data mining, and related subjects.

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