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 | + n c ) space and O ( ( | Q | + d n ) | 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.