url - Universität zu Lübeck

10.4. LIST OF PUBLICATIONS 167
Title: On the Intersection of XPath Expressions
Authors: B. C. Hammerschmidt, M. Kempa and V. Linnemann
Abstract: XPath is a common language for selecting nodes in an XML document. XPath
uses so called path expressions which describe a navigation path through semistructured
data. In the last years some of the characteristics of XPath have been discussed. Examples
include the containment of two XPath expressions p and p ′ (p ⊆ p ′ ). To the best of
our knowledge the intersection of two XPath expressions (p ∩ p ′ ) has not been treated yet.
The intersection of p and p ′ is the set that contains all XML nodes that are selected both
by p and p ′ . In the context of indexes in XML databases the emptiness of the intersection
of p and p ′ is a major issue when updating the index. In order to keep the index consistent
to the indexed data, it has to be detected if an index that is defined upon p is affected by
a modifying database operation with the path expression p ′ .
In this paper we introduce the intersection problem for XPath and give a motivation for its
relevance. We present an efficient intersection algorithm for XPath expressions without
the NOT operator that is based on finite automata. For expressions that contain the NOT
operator the intersection problem becomes NP -complete leading to exponential computations
in general. With an average case simulation we show that the NP -completeness
is no significant limitation for most real-world database operations.
Published: in [46]