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Documents authored by Carstens, Corrie Jacobien

Document
DOI: 10.4230/LIPIcs.ESA.2018.11
Parallel and I/O-efficient Randomisation of Massive Networks using Global Curveball Trades

Authors: Corrie Jacobien Carstens, Michael Hamann, Ulrich Meyer, Manuel Penschuck, Hung Tran, and Dorothea Wagner

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
Graph randomisation is a crucial task in the analysis and synthesis of networks. It is typically implemented as an edge switching process (ESMC) repeatedly swapping the nodes of random edge pairs while maintaining the degrees involved [Mihail and Zegura, 2003]. Curveball is a novel approach that instead considers the whole neighbourhoods of randomly drawn node pairs. Its Markov chain converges to a uniform distribution, and experiments suggest that it requires less steps than the established ESMC [Carstens et al., 2016]. Since trades however are more expensive, we study Curveball's practical runtime by introducing the first efficient Curveball algorithms: the I/O-efficient EM-CB for simple undirected graphs and its internal memory pendant IM-CB. Further, we investigate global trades [Carstens et al., 2016] processing every node in a single super step, and show that undirected global trades converge to a uniform distribution and perform superior in practice. We then discuss EM-GCB and EM-PGCB for global trades and give experimental evidence that EM-PGCB achieves the quality of the state-of-the-art ESMC algorithm EM-ES [M. Hamann et al., 2017] nearly one order of magnitude faster.
Cite as

Corrie Jacobien Carstens, Michael Hamann, Ulrich Meyer, Manuel Penschuck, Hung Tran, and Dorothea Wagner. Parallel and I/O-efficient Randomisation of Massive Networks using Global Curveball Trades. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{carstens_et_al:LIPIcs.ESA.2018.11,
  author =	{Carstens, Corrie Jacobien and Hamann, Michael and Meyer, Ulrich and Penschuck, Manuel and Tran, Hung and Wagner, Dorothea},
  title =	{{Parallel and I/O-efficient Randomisation of Massive Networks using Global Curveball Trades}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.11},
  URN =		{urn:nbn:de:0030-drops-94745},
  doi =		{10.4230/LIPIcs.ESA.2018.11},
  annote =	{Keywords: Graph randomisation, Curveball, I/O-efficiency, Parallelism}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.36
Speeding up Switch Markov Chains for Sampling Bipartite Graphs with Given Degree Sequence

Authors: Corrie Jacobien Carstens and Pieter Kleer

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
We consider the well-studied problem of uniformly sampling (bipartite) graphs with a given degree sequence, or equivalently, the uniform sampling of binary matrices with fixed row and column sums. In particular, we focus on Markov Chain Monte Carlo (MCMC) approaches, which proceed by making small changes that preserve the degree sequence to a given graph. Such Markov chains converge to the uniform distribution, but the challenge is to show that they do so quickly, i.e., that they are rapidly mixing. The standard example of this Markov chain approach for sampling bipartite graphs is the switch algorithm, that proceeds by locally switching two edges while preserving the degree sequence. The Curveball algorithm is a variation on this approach in which essentially multiple switches (trades) are performed simultaneously, with the goal of speeding up switch-based algorithms. Even though the Curveball algorithm is expected to mix faster than switch-based algorithms for many degree sequences, nothing is currently known about its mixing time. On the other hand, the switch algorithm has been proven to be rapidly mixing for several classes of degree sequences. In this work we present the first results regarding the mixing time of the Curveball algorithm. We give a theoretical comparison between the switch and Curveball algorithms in terms of their underlying Markov chains. As our main result, we show that the Curveball chain is rapidly mixing whenever a switch-based chain is rapidly mixing. We do this using a novel state space graph decomposition of the switch chain into Johnson graphs. This decomposition is of independent interest.
Cite as

Corrie Jacobien Carstens and Pieter Kleer. Speeding up Switch Markov Chains for Sampling Bipartite Graphs with Given Degree Sequence. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{carstens_et_al:LIPIcs.APPROX-RANDOM.2018.36,
  author =	{Carstens, Corrie Jacobien and Kleer, Pieter},
  title =	{{Speeding up Switch Markov Chains for Sampling Bipartite Graphs with Given Degree Sequence}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{36:1--36:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.36},
  URN =		{urn:nbn:de:0030-drops-94403},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.36},
  annote =	{Keywords: Binary matrix, graph sampling, Curveball, switch, Markov chain decomposition, Johnson graph}
}
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