TY - GEN A1 - Steinbach, Marc T1 - Topological Index Criteria in DAE for Water Networks N2 - The dynamics of pressurized water distribution networks are naturally modeled by differential algebraic equations (DAE). This paper investigates fundamental structural properties of such a DAE model under weak regularity assumptions. The usual partial derivative-based index-1 condition is shown to be necessary and sufficient for several index concepts, as well as sufficient for solvability in a strong sense. Using the physical properties of nonlinear network elements and the inherent saddle point structure of network hydraulics, we then derive purely topological index criteria based on the network graph and the choice of control variables. Several examples illustrate the theoretical results and explore different non-index-1 situations. A brief discussion of the implications for operative planning by discrete time DAE boundary value problems concludes the paper. T3 - ZIB-Report - 05-49 KW - Water network KW - differential-algebraic equation KW - solvability KW - topological index criteria Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8821 ER - TY - GEN A1 - Djurdjevac Conrad, Natasa A1 - Banisch, Ralf A1 - Schütte, Christof T1 - Modularity of Directed Networks: Cycle Decomposition Approach N2 - The problem of decomposing networks into modules (or clusters) has gained much attention in recent years, as it can account for a coarsegrained description of complex systems, often revealing functional subunits of these systems. A variety of module detection algorithms have been proposed, mostly oriented towards finding hard partitionings of undirected networks. Despite the increasing number of fuzzy clustering methods for directed networks, many of these approaches tend to neglect important directional information. In this paper, we present a novel random walk based approach for finding fuzzy partitions of directed, weighted networks, where edge directions play a crucial role in defining how well nodes in a module are interconnected. We will show that cycle decomposition of a random walk process connects the notion of network modules and information transport in a network, leading to a new, symmetric measure of node communication. Finally, we will use this measure to introduce a communication graph, for which we will show that although being undirected it inherits all necessary information about modular structures from the original network. T3 - ZIB-Report - 14-31 KW - directed networks, modules, cycle decomposition, measure of node communication Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-51166 SN - 1438-0064 ER - TY - GEN A1 - Banisch, Ralf A1 - Schütte, Christof A1 - Djurdjevac Conrad, Natasa T1 - Module Detection in Directed Real-World Networks N2 - We investigate the problem of finding modules (or clusters, communities) in directed networks. Until now, most articles on this topic have been oriented towards finding complete network partitions despite the fact that this often is unwanted. We present a novel random walk based approach for non-complete partitions of the directed network into modules in which some nodes do not belong to only one of the modules but to several or to none at all. The new random walk process is reversible even for directed networks but inherits all necessary information about directions and structure of the original network. We demonstrate the performance of the new method in application to a real-world earthquake network. T3 - ZIB-Report - 14-13 KW - Module identification and classification KW - cycle decomposition KW - communication KW - directed networks Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-49849 SN - 1438-0064 ER - TY - GEN A1 - Koster, Arie M.C.A. A1 - Bodlaender, Hans L. A1 - Hoesel, Stan P.M. van T1 - Treewidth: Computational Experiments N2 - Many {\cal NP}-hard graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to find (almost) optimal solutions or lower bounds for diverse optimization problems. To apply a tree decomposition approach, the treewidth of the graph has to be determined, independently of the application at hand. Although for fixed $k$, linear time algorithms exist to solve the decision problem ``treewidth $\leq k$'', their practical use is very limited. The computational tractability of treewidth has been rarely studied so far. In this paper, we compare four heuristics and two lower bounds for instances from applications such as the frequency assignment problem and the vertex coloring problem. Three of the heuristics are based on well-known algorithms to recognize triangulated graphs. The fourth heuristic recursively improves a tree decomposition by the computation of minimal separating vertex sets in subgraphs. Lower bounds can be computed from maximal cliques and the minimum degree of induced subgraphs. A computational analysis shows that the treewidth of several graphs can be identified by these methods. For other graphs, however, more sophisticated techniques are necessary. T3 - ZIB-Report - 01-38 KW - treewidth KW - heuristics KW - lower bounds KW - computations Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6644 ER -