450 research outputs found
Bisimulations on data graphs
Bisimulation provides structural conditions to characterize indistinguishability from an external observer between nodes on labeled graphs. It is a fundamental notion used in many areas, such as verification, graph-structured databases, and constraint satisfaction. However, several current applications use graphs where nodes also contain data (the so called “data graphs”), and where observers can test for equality or inequality of data values (e.g., asking the attribute ‘name’ of a node to be different from that of all its neighbors). The present work constitutes a first investigation of “data aware” bisimulations on data graphs. We study the problem of computing such bisimulations, based on the observational indistinguishability for XPath —a language that extends modal logics like PDL with tests for data equality— with and without transitive closure operators. We show that in general the problem is PSPACE-complete, but identify several restrictions that yield better complexity bounds (CO- NP, PTIME) by controlling suitable parameters of the problem, namely the amount of non-locality allowed, and the class of models considered (graphs, DAGs, trees). In particular, this analysis yields a hierarchy of tractable fragments.Fil: Abriola, Sergio Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; ArgentinaFil: Barceló, Pablo. Universidad de Chile; ChileFil: Figueira, Diego. Centre National de la Recherche Scientifique; FranciaFil: Figueira, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; Argentin
Benchmarks for Parity Games (extended version)
We propose a benchmark suite for parity games that includes all benchmarks
that have been used in the literature, and make it available online. We give an
overview of the parity games, including a description of how they have been
generated. We also describe structural properties of parity games, and using
these properties we show that our benchmarks are representative. With this work
we provide a starting point for further experimentation with parity games.Comment: The corresponding tool and benchmarks are available from
https://github.com/jkeiren/paritygame-generator. This is an extended version
of the paper that has been accepted for FSEN 201
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
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