### Auflistung nach Schlagwort "graph algorithms"

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- ZeitschriftenartikelNew graph algorithms via polyhedral techniques(it - Information Technology: Vol. 63, No. 3, 2021) Tarnawski, JakubThis article gives a short overview of my dissertation, where new algorithms are given for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. The first part of the dissertation addresses a benchmark problem in combinatorial optimization: the asymmetric traveling salesman problem (ATSP). It consists in finding the shortest tour that visits all vertices of a given edge-weighted directed graph. A ρ -approximation algorithm for ATSP is one that runs in polynomial time and always produces a tour at most ρ times longer than the shortest tour. Finding such an algorithm with constant ρ had been a long-standing open problem. Here we give such an algorithm. The second part of the dissertation addresses the perfect matching problem. We have known since the 1980s that it has efficient parallel algorithms if the use of randomness is allowed. However, we do not know if randomness is necessary – that is, whether the matching problem is in the class NC . We show that it is in the class quasi-NC . That is, we give a deterministic parallel algorithm that runs in poly-logarithmic time on quasi-polynomially many processors.
- TextdokumentUnderstanding Trolls with Efficient Analytics of Large Graphs in Neo4j(BTW 2019, 2019) Allen, David; Hodler, Amy; Hunger, Michael; Knobloch, Martin; Lyon, William; Needham, Mark; Voigt, HannesAnalytics of large graph data set has become an important means of understanding and influencing the world. The use of graph database technology in the International Consortium of Investigative Journalists’ (ICIJ) investigation of the Panama Papers and Paradise Papers or in cancer research illustrates how analysing graph-structured data helps to uncover important but hidden relationships. A very current example in that regards shows how graph analytics can help shed light on the operations of social media troll-networks, e.g. on Twitter. In similar fashion, graph analytics can help enterprises to unearth hidden patterns and structures within connected data, to make more accurate predictions and faster decisions. All this requires efficient graph analytics well-integrated with management of graph data. The Neo4j Graph Platform provides such an environment. It provides transactional processing and analytical processing of graph data including data management and analytics tooling. A central element for graph analytics in the Graph Platform are the Neo4j graph algorithms. Neo4j graph algorithms provide efficiently implemented, parallel versions of common graph algorithms, integrated and optimized for the Neo4j transactional database. In this paper, we will describe the design and integration Neo4j Graph Algorithms, demonstrate its utility of our approach with a Twitter Troll analysis, and show case its performance with a few experiments on large graphs.