André Petermann's research while affiliated with University of Leipzig and other places

... The black dashed edges in the figure provide the output of the link creation. In vertex join as graph fusion [17] (generalized in [6]), the two graphs should be distinct connected components of the same graph and the matching vertices are now fused into one single vertex (Figure 1d). Path joins such as SMJoin [12] are used for traversing one single graph operand at a time [13,21], where each traversed or matched path ⇝ is replaced by one single edge → : this is possible because both the vertex set and edge set are considered as relational tables, and so the path traversal or match can be implemented as a multi-way join producing one single table, thus providing the new edges. ...

... The black dashed edges in the figure provide the output of the link creation. In vertex join as graph fusion [17] (generalized in [6]), the two graphs should be distinct connected components of the same graph and the matching vertices are now fused into one single vertex (Figure 1d). Path joins such as SMJoin [12] are used for traversing one single graph operand at a time [13,21], where each traversed or matched path ⇝ is replaced by one single edge → : this is possible because both the vertex set and edge set are considered as relational tables, and so the path traversal or match can be implemented as a multi-way join producing one single table, thus providing the new edges. ...

... For frequent pattern mining, specialisation involves the extension of the set with a new frequent item [26]. For multi-dimensional frequent sub-graph mining, the specialization entails either the specialization of the nodes appearing in a graph pattern with more specific terms according to a taxonomy [27] or the extension of the graph with further edges and nodes [28]. We can always slightly refine this algorithm to return the S-border containing maximally specific solutions within a data mining solution, thus returning the most specific hypotheses that still satisfy the quality criterion: ...

... While simplistic mining algorithms [20,21,25] enumerate and test all possible hypotheses in L h (Algorithm 1), more efficient ones [5,26,27] represent the whole hypothesis space as a lattice induced by the relationship while traversing from the most general hypothesis ( , Algorithm 2 Line 2) toward the most specific ones, while still validating the quality conditions, which are then returned (Line 7). These last solutions require the definition of a specialization operator ρ. ...

... We have to use the optional RETURN statement if we need to construct a graph as output. The syntax of GQL's RETURN clause is given in Query 4. GQL follows the definition in Cypher and also provides multiple semantics for graph pattern matching [121,122], i.e., isomorphism and homomorphism. In addition, GQL borrows the syntax of regular path expressions from PGQL [66], i.e., "(a:Person)-/:friend_of*/->(a:Person)". ...

... To overcome the limitations of these system approaches and to combine their strengths, we started in 2015 already the development of a new open-source 2 distributed graph analysis platform called Gradoop (Graph Analytics on Hadoop) that has continuously been extended in the last years [29,[39][40][41]43,65,66]. Gradoop is a distributed platform to achieve high scalability and parallel graph processing. ...

... It seems, that around the year 2008 the general interest in novel algorithms faded and many people moved on to parallelizing existing algorithms [cf. 17,27] or solving different problem formulations using variations of the existing algorithms. Jiang et al. [17] concluded in 2013 that this is due to the maturity of the field. ...

... GDBs have been researched in both academia and industry [10,11,75,90,100,124,133], in terms of query languages [7,8,49,208], database management [49, 120,156,172,175], compression and data models [23,35,40,43,146,147,162], execution in novel environments such as the serverless setting [71,150,219], and others [77]. Many graph databases exist [6, 12-15, 46, 55, 56, 59, 65, 73, 78, 82, 87, 89, 125, 126, 151, 154, 155, 164-168, 178, 182, 183, 202, 209, 211, 214, 217, 218, 233, 238, 240]. ...

... Both of our methods are based on the gSpan algorithm [36], in particular an extension supporting directed multigraphs [24]. The most fundamental component of gSpan is the use of DFS codes to represent graph patterns in a canonical form. ...

... The foundation of GRADOOP is ongoing research in the fields of graph data management, graph analytics and graph mining. Regarding the latter, we investigate in methods using more meaningful interestingness measures than minimum support, for example, to identify patterns correlating with certain business measure values [20]. Due to the huge data volume in many applications and the high computational complexity of graph pattern mining, our second focus is the efficient parallelization of graph algorithms using shared-nothing clusters. ...