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We study a graph-augmentation problem arising from a technique applied in recent approaches for route planning. Many such methods enhance the graph by inserting shortcuts, i.e., additional edges (u, v) such that the length of (u, v) is the distance from u to v. Given a weighted, directed graph G and a number c ∈ Z >0 , the shortcut problem asks how to… (More)

Clustering a graph means identifying internally dense subgraphs that are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find clusterings. Since, most generally, corresponding optimization problems are hard, heuristic clustering algorithms are used in… (More)

Maximizing the quality index <i>modularity</i> has become one of the primary methods for identifying the clustering structure within a graph. Since many contemporary networks are not static but evolve over time, traditional static approaches can be inappropriate for specific tasks. In this work, we pioneer the NP-hard problem of online dynamic modularity… (More)

—Collaboration networks arise when we map the connections between scientists which are formed through joint publications. These networks thus display the social structure of academia, and also allow conclusions about the structure of scientific knowledge. Using the computer science publication database DBLP, we compile relations between authors and… (More)

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