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Extra info for A density lemma
Other summaries are augmented with statistical information of the instance for selectivity estimation, including path/branching distribution (XSketch ), value distributions , and additional statistical information for approximate query processing . 8 Conclusion and Future Work The paper introduces DescribeX, a novel framework for describing structural summaries of XML collections. Summary partitions are deﬁned by AxPRE’s created from arbitrary XPath queries, supporting fast evaluation of complex XPath workloads over large web document collections.
Given an arbitrary XPath query, DescribeX can create a partition deﬁned by an AxPRE that captures exactly the structural commonality expressed by the query. This paper presents experimental results that demonstrate that using a summary created from a given workload can produce query evaluation times orders of magnitude better than using existing summaries. The experiments also validate that DescribeX summaries allow ﬁle at a time XPath processors to be a competitive alternative (in terms of performance) to DB-like XML query engines – even on gigabyte sized collections.
However, according to Deﬁnition 4, they are bisimilar and thus nodes 18 and 24 belong to the same extent (that of node s62 in Figure 2 (b)). f s (24). Consequently, node 6 is assigned to a diﬀerent extent (that of node s61 in Figure 2 (b)). A bisimulation provides a way of computing a double homomorphism between graphs. The widespread use of bisimulation in summaries is motivated by its relatively low computational complexity properties. The bisimulation reduction of a labelled graph can be done in time O(m log m) (where m is the number of edges in a labelled graph) as shown in , or even linearly for acyclic graphs, as shown in .
A density lemma