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- Ulrik Brandes, Daniel Delling, +4 authors Dorothea Wagner
- IEEE Transactions on Knowledge and Data…
- 2008

Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, particularly in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations for… (More)

- Thomas Schank, Dorothea Wagner
- WEA
- 2005

In the past, the fundamental graph problem of triangle counting and listing has been studied intensively from a theoretical point of view. Recently, triangle counting has also become a widely used tool in network analysis. Due to the very large size of networks like the Internet, WWW, or social networks, the efficiency of algorithms for triangle counting… (More)

As the amount of data we nowadays have to deal with becomes larger and larger, the methods that help us to detect structures in the data and to identify interesting subsets in the data become more and more important. One of these methods is clustering, i.e. segmenting a set of elements into subsets such that the elements in each subset are somehow… (More)

- Frank Schulz, Dorothea Wagner, Karsten Weihe
- Algorithm Engineering
- 1999

Traffic information systems are among the most prominent real-world applications of Dijkstra's algorithm for shortest paths. We consider the scenario of a central information server in the realm of public railroad transport on wide-area networks. Such a system has to process a large number of on-line queries for optimal travel connections in real time. In… (More)

- Evangelia Pyrga, Frank Schulz, Dorothea Wagner, Christos D. Zaroliagis
- ACM Journal of Experimental Algorithmics
- 2007

We consider two approaches that model timetable information in public transportation systems as shortest-path problems in weighted graphs. In the <i>time-expanded</i> approach, every event at a station, e.g., the departure of a train, is modeled as a node in the graph, while in the <i>time-dependent</i> approach the graph contains only one node per station.… (More)

- Ulrik Brandes, Daniel Delling, +4 authors Dorothea Wagner
- WG
- 2007

Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, and in particular in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations… (More)

- Martin Holzer, Frank Schulz, Dorothea Wagner
- ACM Journal of Experimental Algorithmics
- 2006

An overlay graph of a given graph <i>G</i> = (<i>V</i>, <i>E</i>) on a subset <i>S</i> ⊆ <i>V</i> is a graph with vertex set <i>S</i> and edges corresponding to shortest paths in <i>G</i>. In particular, we consider variations of the multilevel overlay graph used in Schulz et al. [2002] to speed up shortest-path computation. In this work, we… (More)

This paper studies the problem of computing optimal journeys in dynamic public transit networks. We introduce a novel algorithmic framework, called Connection Scan Algorithm (CSA), to compute journeys. It organizes data as a single array of connections, which it scans once per query. Despite its simplicity, our algorithm is very versatile. We use it to… (More)

- Daniel Delling, Dorothea Wagner
- WEA
- 2007

Many speed-up techniques for route planning in static graphs exist, only few of them are proven to work in a dynamic scenario. Most of them use preprocessed information, which has to be updated whenever the graph is changed. However, goal directed search based on landmarks (ALT) still performs correct queries as long as an edge weight does not drop below… (More)

- Ulrik Brandes, Marco Gaertler, Dorothea Wagner
- ESA
- 2003

A promising approach to graph clustering is based on the intuitive notion of intra-cluster density vs. inter-cluster sparsity. While both formalizations and algorithms focusing on particular aspects of this rather vague concept have been proposed no conclusive argument on their appropriateness has been given. As a first step towards understanding the… (More)