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10
Indexing Structure for Graph-Structured Data
Stanislav Barton and Pavel Zezula
Faculty of Informatics, Masaryk University
Botanicka 68a, 60200 Brno
Czech Republic
{ barton, zezula } @fi.muni.cz
Abstract. An own design of an indexing structure for general graph structured data
called ρ -index that allows an effective processing of special path queries is presented.
These special queries represent for example a search for all paths lying between two
arbitrary vertices limited to a certain path length. The ρ -index is a multilevel balanced
tree structure where each node is created with a certain graph transformation and
described by modified adjacency matrix. Hence, ρ -index indexes all the paths to a
predefined length l inclusive. The search algorithm is then able to find all the paths
shorter than or having the length l and some of the paths longer then the predefined
l lying between any two vertices in the indexed graph. The designed search algorithm
exploits a special graph structure, a transcription graph, to compute the result using
the ρ -index . We also present an experimental evaluation of the process of creating the
ρ -index on graphs with different sizes and also a complexity evaluation of the search
algorithm that uses the ρ -index.
10.1
Introduction
In the context of the Semantic Web, ρ -operators are proposed in [5] as a mean to
explore complex relationships [20] between entities. The problem of searching for
the complex relationships can be modeled as the process of searching paths in a
graph where various entities represent vertices and edges the direct relationships
between them. In case of the semantic web the resources or classes and edges
the properties between them. The notion of complex relationships can be also
identified in bibliographic digital libraries, where entities are publications and
the relationship can represent references or direct citations between them.
As proposed in [5], we recognize two kinds of complex relationships. The first
one is represented by apath lying between two inspected vertices. Speaking in
terms of publications this means that one publication indirectly cites or refer-
ences the other publication - a chain of publications can be built so that one
cites another. The second type of complex relationship is a connection between
two inspected vertices. This symbolizes a fact that the two inspected publica-
tions indirectly cite one common publication, see Figure 10.1 for an example of
this kind of complex relationship.
 
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