25.06.2019

Paper accepted at ESA

The European Symposium on Algorithms (ESA) is the premier algorithms conference in Europe, it will be held as part of the ALGO 2019 Meeting September 9-13 in Munich, Germany. The Algorithm Engineering group contributes one paper together with colleagues of the Goethe University Frankfurt. The work describes the development, implementation, and testing of the world's fastest algorithm for generating Geometric Inhomogeneous Random Graphs (GIRGs) as well as Hyperbolic Randon Graphs (HRGs).

Clean Citation Style 005

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Bläsius, Thomas; Friedrich, Tobias; Katzmann, Maximilian; Meyer, Ulrich; Penschuck, Manuel; Weyand, Christopher Efficiently Generating Geometric Inhomogeneous and Hyperbolic Random GraphsEuropean Symposium on Algorithms (ESA) 2019: 21:2–21:14

[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]

@inproceedings{blaesius2019efficiently,
  abstract = {Hyperbolic random graphs (HRG) and geometric inhomogeneous random graphs (GIRG) are two similar generative network models that were designed to resemble complex real world networks. In particular, they have a power-law degree distribution with controllable exponent \(\beta\), and high clustering that can be controlled via the temperature \(T\). We present the first implementation of an efficient GIRG generator running in expected linear time. Besides varying temperatures, it also supports underlying geometries of higher dimensions. It is capable of generating graphs with ten million edges in under a second on commodity hardware. The algorithm can be adapted to HRGs. Our resulting implementation is the fastest sequential HRG generator, despite the fact that we support non-zero temperatures. Though non-zero temperatures are crucial for many applications, most existing generators are restricted to \(T = 0\). We also support parallelization, although this is not the focus of this paper. Moreover, we note that our generators draw from the correct probability distribution, i.e., they involve no approximation. Besides the generators themselves, we also provide an efficient algorithm to determine the non-trivial dependency between the average degree of the resulting graph and the input parameters of the GIRG model. This makes it possible to specify \(\bar{d}\) as input and obtain a graph with expected average degree \(\bar{d}\). Moreover, we investigate the differences between HRGs and GIRGs, shedding new light on the nature of the relation between the two models. Although HRGs represent, in a certain sense, a special case of the GIRG model, we find that a straight-forward inclusion does not hold in practice. However, the difference is negligible for most use cases.},
  author = {Bläsius, Thomas and Friedrich, Tobias and Katzmann, Maximilian and Meyer, Ulrich and Penschuck, Manuel and Weyand, Christopher},
  booktitle = {European Symposium on Algorithms (ESA)},
  keywords = {christopherweyand esa hyperbolic_generation manuelpenschuck maximiliankatzmann thomasblaesius tobiasfriedrich ulrichmeyer year2019},
  note = {EATCS Best Paper Award},
  pages = {21:2-21:14},
  title = {Efficiently Generating Geometric Inhomogeneous and Hyperbolic Random Graphs},
  year = 2019
}