A hierarchy of increasingly coarse versions of a network allows one to represent the network on multiple scales at the same time. Often, the elementary operation for generating a hierarchy on a network is merging adja...
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A hierarchy of increasingly coarse versions of a network allows one to represent the network on multiple scales at the same time. Often, the elementary operation for generating a hierarchy on a network is merging adjacent vertices, an operation that can be realized through contracting the edge between the two vertices. Such a hierarchy is defined by the selection of the edges to be contracted between a level and the next coarser level. The selection may involve (i) rating the edges, (ii) constraining the selection (e.g., that the selected edges form a matching), as well as (iii) maximizing the total rate of the selected edges under the constraints. Hierarchies of this kind are, among others, involved in multilevel methods for partitioning networks-a prerequisite for processing in parallel with distributed memory. In this article, we propose a new edge rating by (i) defining weights for the edges of a network that express the edges' importance for connectivity via shortest paths, (ii) computing a minimum weight spanning tree with respect to these weights, and (iii) rating the network edges based on the conductance values of the tree's fundamental cuts. To make the computation of our new edge rating efficient,we develop the first optimal linear-time algorithm to compute the conductance values of all fundamental cuts of a given spanning tree. We integrate the new edge rating into a leading multilevel graph partitioner and equip the latter also with a new greedy postprocessing for optimizing the Maximum Communication Volume (MCV) of a partition. Our experiments, in which we bipartition frequently used benchmark networks, show that the postprocessing reduces MCV by 11.3%. Our new edge rating, here used for matching-based coarsening, further reduces MCV by 10.3% compared to the previously best rating with MCV postprocessing in place for both ratings. In total, with a modest increase in running time, our new approach reduces the MCV of complex network partitions by 20.4%.
A systematic procedure for sensitivity analysis of a case study in the area of air pollution modeling has been performed. Contemporary mathematical models should include a large set of chemical and photochemical react...
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Grid portals are increasingly used to provide uniform access to the grid infrastructure. This paper describes how the P-GRADE Grid Portal could be used in a collaborative manner to facilitate group work and support th...
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The DTN Dataflow Computer is a graphics workstation containing 32 dataflow processing elements. It may possibly be the first commercially available dataflow machine. In this article our main focus is on its RC compile...
The DTN Dataflow Computer is a graphics workstation containing 32 dataflow processing elements. It may possibly be the first commercially available dataflow machine. In this article our main focus is on its RC compiler. Although dataflow machines are usually programmed in a declarative language, RC is imperative: it is a somewhat restricted form of C. The main problems encountered during the implementation of the compiler were due to the low level of the instruction set of the dataflow processors: these were not designed as target for a high-level language. Consequently generating efficient code for general features such as conditionals and loops required a substantial effort. Surprisingly, most imperative features were easy to deal with. The most serious problem still awaiting an efficient solution is conditional aliasing.
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