Worst-case optimal algorithm for XPath evaluation over XML streams

Abstract

We consider the XPath evaluation problem: Evaluate an XPath query Q on a streaming XML document D; i.e., determine the set Q (D) of document elements selected by Q . We mainly consider Conjunctive XPath queries that involve only the child and descendant axes. Previously known in-memory algorithms for this problem use O (|D|) space and O (|Q ||D|) time. Several previously known algorithms for the streaming version use Ω(d n ) space and Ω(d n |D|) time in the worst case; d denotes the depth of D, and n denotes the number of location steps in Q . Their exponential space requirement could well exceed the O (|D|)space used by the in-memory algorithms. We present an efficient algorithm that uses O (d|Q | + nc) space and O ((|Q | + dn)|D|) time in the worst case; c denotes the maximum number of elements of D that can be candidates for output, at any one instant. For some worst case Q and D, the memory space used by our algorithm matches our lower bound proved in a different paper; so, our algorithm uses optimal memory space in the worst case.

Streamable Fragments of Forward XPath

“…This shows that the memory consumption of the two algorithms of [2] and [12] cannot be polynomial in the number of alive candidates, in contrast to what is stated there 4 except if P=NP. We also note that streaming algorithms for Forward XPath in [22] and [23,24] do not claim finite streamability. The complexity results stated there count the maximal number of candidates stored simultaneously by their algorithms, rather than the maximal number of alive candidates with respect to the query.…”

“…Query answering algorithms for XPath on Xml streams received much interest in the database and document processing communities [2,24,3,22,5,12,29,6,21] and are currently in the focus of the W3C working groups on Xslt and Xproc [14]. A little surprisingly, the topic is far from being settled given the large remaining gap between known streamable and non-streamable fragments.…”

Path stream group level encoding: Efficient wireless XML streaming

“…Streaming algorithms broadly fall in three categories: the automaton-based approach [6,9,11,18], the array-based approach [4], and the stackbased approach [12,13,14,16,21,24].…”

“…A number of more recent algorithms [12,13,16,21,24] exploit its ideas in order to evaluate TPQs on streaming XML data. These stack-based algorithms extend PathStack to compactly encode query pattern matches in a chain of stacks.…”

“…Streaming algorithms for processing XPath queries that involve only downward un-ordered XPath axes (child, descendant) can be extended for handling XPath queries with ordered axes (following-sibling, following, preceding-sibling, and preceding) [18,22,23,24]. Lineage Encoding focuses on twig pattern queries [28] and considers grouping of nodes based on node name alone.…”