Finding all the occurrences of a twig pattern specified by a selection predicate on multiple elements in an XML document is a core operation for efficient evaluation of XML queries. Holistic twig join algorithms were proposed recently as an optimal solution when the twig pattern only involves ancestordescendant relationships. In this paper, we address the problem of efficient processing of holistic twig joins on all/partly indexed XML documents. In particular, we propose an algorithm that utilizes available indices on element sets. While it can be shown analytically that the proposed algorithm is as efficient as the existing state-of-the-art algorithms in terms of worst case I/O and CPU cost, experimental results on various datasets indicate that the proposed index-based algorithm performs significantly better than the existing ones, especially when binary structural joins in the twig pattern have varying join selectivities.

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Most of the previous studies on mining association rules are on mining intratransaction associations, i.e., the associations among items within the same transaction where the notion of the transaction could be the items bought by the same customer, the events happened on the same day, etc. In this study, we break the barrier of transactions and extend the scope of mining association rules from traditional single-dimensional, intratransaction associations to multidimensional, intertransaction associations. An intertransaction association describes the association relationships among different transactions. In a database of stock price information, an example of such an association is "if (company) A's stock goes up on day one, B's stock will go down on day two but go up on day four." In this case, no matter whether we treat company or day as the unit of transaction, the associated items belong to different transactions. Moreover, such an intertransaction association can be extended to associate multiple properties in the same rule, so that multidimensional intertransaction associations can also be defined and discovered. Mining intertransaction associations pose more challenges on efficient processing than mining intratransaction associations because the number of potential association rules becomes extremely large after the boundary of transactions is broken. In this study, we introduce the notion of intertransaction association rule, define its measurements: support and confidence, and develop an efficient algorithm, FITI (an acronym for "First Intra Then Inter"), for mining intertransaction associations, which adopts two major ideas: 1) an intertransaction frequent itemset contains only the frequent itemsets of its corresponding intratransaction counterpart; and 2) a special data structure is built among intratransaction frequent itemsets for efficient mining of intertransaction frequent itemsets. We compare FITI with EH-Apriori, the best algorithm in our previous proposal, and demonstrate a substantial performance gain of FITI over EH-Apriori. Further extensions of the method and its implications are also discussed in the paper.

Statistics over the most recently observed data elements are often required in applications involving data streams, such as intrusion detection in network monitoring, stock price prediction in financial markets, web log mining for access prediction, and user click stream mining for personalization. Among various statistics, computing quantile summary is probably most challenging because of its complexity. In this paper, we study the problem of continuously maintaining quantile summary of the most recently observed N elements over a stream so that quantile queries can be answered with a guaranteed precision of ǫN . We developed a space efficient algorithm for pre-defined N that requires only one scan of the input data stream and O( log(ǫ 2 N ) ǫ + 1 ǫ 2 ) space in the worst cases. We also developed an algorithm that maintains quantile summaries for most recent N elements so that quantile queries on any most recent n elements (n ≤ N ) can be answered with a guaranteed precision of ǫn. The worst case space requirement for this algorithm is only O( log 2 (ǫN ) ǫ 2). Our performance study indicated that not only the actual quantile estimation error is far below the guaranteed precision but the space requirement is also much less than the given theoretical bound.