1 research outputs found
Time and Memory Efficient Parallel Algorithm for Structural Graph Summaries and two Extensions to Incremental Summarization and -Bisimulation for Long -Chaining
We developed a flexible parallel algorithm for graph summarization based on
vertex-centric programming and parameterized message passing. The base
algorithm supports infinitely many structural graph summary models defined in a
formal language. An extension of the parallel base algorithm allows incremental
graph summarization. In this paper, we prove that the incremental algorithm is
correct and show that updates are performed in time , where is the number of additions, deletions, and modifications
to the input graph, the maximum degree, and is the maximum distance in
the subgraphs considered. Although the iterative algorithm supports values of
, it requires nested data structures for the message passing that are
memory-inefficient. Thus, we extended the base summarization algorithm by a
hash-based messaging mechanism to support a scalable iterative computation of
graph summarizations based on -bisimulation for arbitrary . We
empirically evaluate the performance of our algorithms using benchmark and
real-world datasets. The incremental algorithm almost always outperforms the
batch computation. We observe in our experiments that the incremental algorithm
is faster even in cases when of the graph database changes from one
version to the next. The incremental computation requires a three-layered hash
index, which has a low memory overhead of only (). Finally, the
incremental summarization algorithm outperforms the batch algorithm even with
fewer cores. The iterative parallel -bisimulation algorithm computes
summaries on graphs with over M edges within seconds. We show that the
algorithm processes graphs of M edges within a few minutes while having
a moderate memory consumption of GB. For the largest BSBM1B dataset with
1 billion edges, it computes bisimulation in under an hour