Article
Aggregation and Numerical Techniques for Passage Time Calculations in Large semiMarkov Models
07/2009;
 Citations (18)
 Cited In (0)

Conference Paper: Graph Partitioning and Parallel Solvers: Has the Emperor No Clother? (Extended Abstract).
Solving Irregularly Structured Problems in Parallel, 5th International Symposium, IRREGULAR '98, Berkeley, California, USA, August 911, 1998, Proceedings; 01/1998 
Article: A TwoDimensional Data Distribution Method for Parallel Sparse MatrixVector Multiplication
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ABSTRACT: A new method is presented for distributing data in sparse matrixvector multiplication. The method is twodimensional, tries to minimize the true communication volume, and also tries to spread the computation and communication work evenly over the processors. The method starts with a recursive bipartitioning of the sparse matrix, each time splitting a rectangular matrix into two parts with a nearly equal number of nonzeros. The communication volume caused by the split is minimized. After the matrix partitioning, the input and output vectors are partitioned with the objective of minimizing the maximum communication volume per processor. Experimental results of our implementation, Mondriaan, for a set of sparse test matrices show a reduction in communication volume compared to onedimensional methods, and in general a good balance in the communication work. Experimental timings of an actual parallel sparse matrixvector multiplication on an SGI Origin 3800 computer show that a sufficiently large reduction in communication volume leads to savings in execution time.SIAM Review 06/2002; · 5.95 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: SemiMarkov modelling paradigms are more expressive than their Markovian counterparts but are equally vulnerable to the state space explosion problem. This paper addresses this issue by presenting an exact statebystate aggregation algorithm for semiMarkov mod els. Empirical evidence shows that the computational complexity of our method depends critically on the order in which the states are aggregated. We investigate different stateordering strategies and find one that aggregates a large proportion (circa 75%) of our exam ple state spaces at minimal cost. This leaves a significa ntly smaller model which can then be analysed for performancerelated quanti ties such as passagetime quantiles. We demonstrate our technique on several examples, including a state model which is re duced to states.
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