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Showing papers by "Ulrich Meyer published in 2012"


Proceedings ArticleDOI
12 Nov 2012
TL;DR: It is shown that transfer entropy values peak if the delay of the state of the driving system equals the true interaction delay, and reconstructed delays from a bivariate transfer entropy analysis of a network can be used to label spurious interactions arising from cascade effects.
Abstract: To understand the function of networks we have to identify the structure of their interactions, but also interaction timing, as compromised timing of interactions may disrupt network function. We demonstrate how both questions can be addressed using a modified estimator of transfer entropy. Transfer entropy is an implementation of Wiener's principle of observational causality based on information theory, and detects arbitrary linear and non-linear interactions. Using a modified estimator that uses delayed states of the driving system and independently optimized delayed states of the receiving system, we show that transfer entropy values peak if the delay of the state of the driving system equals the true interaction delay. In addition, we show how reconstructed delays from a bivariate transfer entropy analysis of a network can be used to label spurious interactions arising from cascade effects and apply this approach to local field potential (LFP) and magnetoencephalography (MEG) data.

15 citations


Journal ArticleDOI
TL;DR: I/O-efficient single-source shortest path algorithms for undirected graphs with expected I/O complexity O(&sqrt;(nm log B) + MST(n, m) for uniformly random edge lengths.
Abstract: We present I/O-efficient single-source shortest path algorithms for undirected graphs. Our main result is an algorithm with I/O complexity O(√(nmlog L)/B+MST(n, m)) on graphs with n vertices, m edges, and arbitrary edge lengths between 1 and L; MST(n, m denotes the I/O complexity of computing a minimum spanning tree; B denotes the disk block size. If the edge lengths are drawn uniformly at random from (0,1], the expected I/O complexity of the algorithm is O(√nm/B + (m/B)log B + MST(n, m)). A simpler algorithm has expected I/O complexity O(√(nm log B)/B + MST(n, m)) for uniformly random edge lengths.

13 citations


Book ChapterDOI
10 Sep 2012
TL;DR: It is shown that the hierarchical approach is frequently capable of producing surprisingly good diameter approximations in shorter time than BFS, and provides theoretical and practical insights into worst-case input classes.
Abstract: Computing diameters of huge graphs is a key challenge in complex network analysis. As long as the graphs fit into main memory, diameters can be efficiently approximated (and frequently even exactly determined) using heuristics that apply a limited number of BFS traversals. If the input graphs have to be kept and processed on external storage, even a single BFS run may cause an unacceptable amount of time-consuming I/O-operations. Meyer [17] proposed the first parameterized diameter approximation algorithm with fewer I/Os than that required for exact BFS traversal. In this paper we derive hierarchical extensions of this randomized approach and experimentally compare their trade-offs between actually achieved running times and approximation ratios. We show that the hierarchical approach is frequently capable of producing surprisingly good diameter approximations in shorter time than BFS. We also provide theoretical and practical insights into worst-case input classes.

8 citations


Journal ArticleDOI
TL;DR: Efficient algorithms to analyze the cycle structure of the graph induced by the state transition function of the A5/1 stream cipher used in GSM mobile phones are described and structural results for the full graph are presented for the first time.
Abstract: We describe efficient algorithms to analyze the cycle structure of the graph induced by the state transition function of the A5/1 stream cipher used in GSM mobile phones and report on the results of the implementation. The analysis is performed in five steps utilizing HPC clusters, GPGPU and external memory computation. A great reduction of this huge state transition graph of 2^64 nodes is achieved by focusing on special nodes in the first step and removing leaf nodes that can be detected with limited effort in the second step. This step does not break the overall structure of the graph and keeps at least one node on every cycle. In the third step the nodes of the reduced graph are connected by weighted edges. Since the number of nodes is still huge an efficient bitslice approach is presented that is implemented with NVIDIA's CUDA framework and executed on several GPUs concurrently. An external memory algorithm based on the STXXL library and its parallel pipelining feature further reduces the graph in the fourth step. The result is a graph containing only cycles that can be further analyzed in internal memory to count the number and size of the cycles. This full analysis which previously would take months can now be completed within a few days and allows to present structural results for the full graph for the first time. The structure of the A5/1 graph deviates notably from the theoretical results for random mappings.

8 citations


Journal ArticleDOI
21 Jun 2012
TL;DR: An implementation of Meyer's proposed parametrized algorithm to compute an approximation of graph diameter with fewer I/Os than that required for exact BFS traversal of the graph is presented and it is confirmed that there are graph-classes where the parametRIzed approach runs into bad approximation ratios just as the theoretical analysis in (Meyer, 2008) suggests.
Abstract: A fundamental step in the analysis of a massive graph is to compute its diameter. In the RAM model, the diameter of a connected undirected unweighted graph can be efficiently 2-approximated using a Breadth-First Search (BFS) traversal from an arbitrary node. However, if the graph is stored on disk, even an external memory BFS traversal is prohibitive, owing to the large number of I/Os it incurs. Meyer [1] proposed a parametrized algorithm to compute an approximation of graph diameter with fewer I/Os than that required for exact BFS traversal of the graph. The approach is based on growing clusters around randomly chosen vertices ‘in parallel’ until their fringes meet. We present an implementation of this algorithm and compare it with some simple heuristics and external-memory BFS in order to determine the trade-off between the approximation ratio and running-time achievable in practice. Our experiments show that with carefully chosen parameters, the new approach is indeed capable to produce surprisingly good diameter approximations in shorter time. We also confirm experimentally, that there are graph-classes where the parametrized approach runs into bad approximation ratios just as the theoretical analysis in [1] suggests.

6 citations


Journal ArticleDOI
23 Oct 2012
TL;DR: In this paper, the authors describe efficient algorithms to analyze the cycle structure of the graph induced by the state transition function of the A5/1 stream cipher used in GSM mobile phones.
Abstract: We describe efficient algorithms to analyze the cycle structure of the graph induced by the state transition function of the A5/1 stream cipher used in GSM mobile phones and report on the results of the implementation. The analysis is performed in five steps utilizing HPC clusters, GPGPU and external memory computation. A great reduction of this huge state transition graph of 2 64 nodes is achieved by focusing on special nodes in the first step and removing leaf nodes that can be detected with limited effort in the second step. This step does not break the overall structure of the graph and keeps at least one node on every cycle. In the third step the nodes of the reduced graph are connected by weighted edges. Since the number of nodes is still huge an efficient bitslice approach is presented that is implemented with NVIDIA’s CUDA framework and executed on several GPUs concurrently. An external memory algorithm based on the STXXL library and its parallel pipelining feature further reduces the graph in the fourth step. The result is a graph containing only cycles that can be further analyzed in internal memory to count the number and size of the cycles. This full analysis which previously would take months can now be completed within a few days and allows to present structural results for the full graph for the first time. The structure of the A5/1 graph deviates notably from the theoretical results for random mappings.

5 citations


Proceedings Article
01 Oct 2012
TL;DR: In this article, the authors describe efficient algorithms to analyze the cycle structure of the graph induced by the state transition function of the A5/1 stream cipher used in GSM mobile phones.
Abstract: We describe efficient algorithms to analyze the cycle structure of the graph induced by the state transition function of the A5/1 stream cipher used in GSM mobile phones and report on the results of the implementation. The analysis is performed in five steps utilizing HPC clusters, GPGPU and external memory computation. A great reduction of this huge state transition graph of 2 64 nodes is achieved by focusing on special nodes in the first step and removing leaf nodes that can be detected with limited effort in the second step. This step does not break the overall structure of the graph and keeps at least one node on every cycle. In the third step the nodes of the reduced graph are connected by weighted edges. Since the number of nodes is still huge an efficient bitslice approach is presented that is implemented with NVIDIA’s CUDA framework and executed on several GPUs concurrently. An external memory algorithm based on the STXXL library and its parallel pipelining feature further reduces the graph in the fourth step. The result is a graph containing only cycles that can be further analyzed in internal memory to count the number and size of the cycles. This full analysis which previously would take months can now be completed within a few days and allows to present structural results for the full graph for the first time. The structure of the A5/1 graph deviates notably from the theoretical results for random mappings.

3 citations