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On the complexity of strongly connected components in directed hypergraphs
 Algorithmica
"... Abstract. We study the problem of determining strongly connected components (Sccs) of directed hypergraphs. The main contribution is an algorithm computing the terminal strongly connected components (i.e. Sccs which do not reach any other components than themselves). The time complexity of the algo ..."
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Abstract. We study the problem of determining strongly connected components (Sccs) of directed hypergraphs. The main contribution is an algorithm computing the terminal strongly connected components (i.e. Sccs which do not reach any other components than themselves). The time complexity of the algorithm is almost linear, which is a significant improvement over the known methods which are quadratic time. This also proves that the problems of (i) testing strong connectivity, (ii) and determining the existence of a sink, can be both solved in almost linear time in directed hypergraphs. We also highlight an important discrepancy between the reachability relations in directed hypergraphs and graphs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. We also prove linear time reductions from combinatorial problems on the subset partial order, in particular from the wellstudied problem of finding all minimal sets among a given family, to the problem of computing the Sccs in directed hypergraphs. 1.
THEME Modeling, Optimization, and Control of Dynamic SystemsTable of contents
"... 4.3. Switched systems 5 5. Software................................................................................. 6 6. New Results.............................................................................. 6 6.1. New results: geometric control 6 6.2. New results: quantum control 8 6.3. New res ..."
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4.3. Switched systems 5 5. Software................................................................................. 6 6. New Results.............................................................................. 6 6.1. New results: geometric control 6 6.2. New results: quantum control 8 6.3. New results: neurophysiology 8 6.4. New results: switched systems 9
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"... The main contributions that are put forward in this thesis will be described shortly. 1. Instead of computing the largest 2club in a network, all 2clubs in a network are computed. In addition, this set of 2clubs is classified, ordered and clustered. Here the characterization by Mokken [13] is use ..."
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The main contributions that are put forward in this thesis will be described shortly. 1. Instead of computing the largest 2club in a network, all 2clubs in a network are computed. In addition, this set of 2clubs is classified, ordered and clustered. Here the characterization by Mokken [13] is used. 2. The running times of the known algorithms and the ones proposed this thesis are evaluated on random graphs that were also used by Bourjolly [5]. Additional experiments are performed on a number of representative real world examples. 3. A parallel version of the branch an bound approach of Bourjolly [5] has been implemented and the effect of adding extra cores on the running times is evaluated. 4. The branch and bound method of Bourjolly [5] can be transformed to matrix algebra and in the case of 2clubs, it can be simplified using the decomposition of the square of the adjacency matrix. The enhanced algorithm
Mining MassiveScale Spatiotemporal Trajectories in Parallel: A Survey
"... Abstract. With the popularization of positioning devices such as GPS navigators and smart phones, large volumes of spatiotemporal trajectory data have been produced at unprecedented speed. For many trajectory mining problems, a number of computationally efficient approaches have been proposed. How ..."
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Abstract. With the popularization of positioning devices such as GPS navigators and smart phones, large volumes of spatiotemporal trajectory data have been produced at unprecedented speed. For many trajectory mining problems, a number of computationally efficient approaches have been proposed. However, to more effectively tackle the challenge of big data, it is important to exploit various advanced parallel computing paradigms. In this paper, we present a comprehensive survey of the stateoftheart techniques for mining massivescale spatiotemporal trajectory data based on parallel computing platforms such as Graphics Processing Unit (GPU), MapReduce and Field Programmable Gate Array (FPGA). This survey covers essential topics including trajectory indexing and query, clustering, join, classification, pattern mining and applications. We also give an indepth analysis of the related techniques and compare them according to their principles and performance.