Browsing by Subject "Iterative Methods"

Now showing 1 - 5 of 5

Open Access
Automated construction of fuzzy event sets and its application to active databases
(IEEE, 2001) Saygin, Y.; Ulusoy, Özgür
Fuzzy sets and fuzzy logic research aims to bridge the gap between the crisp world of math and the real world. Fuzzy set theory was applied to many different areas, from control to databases. Sometimes the number of events in an event-driven system may become very high and unmanageable. Therefore, it is very useful to organize the events into fuzzy event sets also introducing the benefits of the fuzzy set theory. All the events that have occurred in a system can be stored in event histories which contain precious hidden information. In this paper, we propose a method for automated construction of fuzzy event sets out of event histories via data mining techniques. The useful information hidden in the event history is extracted into a matrix called sequential proximity matrix. This matrix shows the proximities of events and it is used for fuzzy rule execution via similarity based event detection and construction of fuzzy event sets. Our application platform is active databases. We describe how fuzzy event sets can be exploited for similarity based event detection and fuzzy rule execution in active database systems.
Open Access
Comparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chains
(SIAM, 2000) Dayar T.; Stewart, W. J.
Experimental results for large, sparse Markov chains, especially the ill-conditioned nearly completely decomposable (NCD) ones, are few. We believe there is need for further research in this area, specifically to aid in the understanding of the effects of the degree of coupling of NCD Markov chains and their nonzero structure on the convergence characteristics and space requirements of iterative solvers. The work of several researchers has raised the following questions that led to research in a related direction: How must one go about partitioning the global coefficient matrix into blocks when the system is NCD and a two-level iterative solver (such as block SOR) is to be employed? Are block partitionings dictated by the NCD form of the stochastic one-step transition probability matrix necessarily superior to others? Is it worth investigating alternative partitionings? Better yet, for a fixed labeling and partitioning of the states, how does the performance of block SOR (or even that of point SOR) compare to the performance of the iterative aggregation-disaggregation (IAD) algorithm? Finally, is there any merit in using two-level iterative solvers when preconditioned Krylov subspace methods are available? We seek answers to these questions on a test suite of 13 Markov chains arising in 7 applications.
Open Access
Iterative disaggregation for a class of lumpable discrete-time stochastic automata networks
(Elsevier, 2003) Gusak, O.; Dayar T.; Fourneau, J. M.
Stochastic automata networks (SANs) have been developed and used in the last 15 years as a modeling formalism for large systems that can be decomposed into loosely connected components. In this work, we concentrate on the not so much emphasized discrete-time SANs. First, we remodel and extend an SAN that arises in wireless communications. Second, for an SAN with functional transitions, we derive conditions for a special case of ordinary lumpability in which aggregation is done automaton by automaton. Finally, for this class of lumpable discrete-time SANs we devise an efficient aggregation-iterative disaggregation algorithm and demonstrate its performance on the SAN model of interest. © 2002 Elsevier Science B.V. All rights reserved.
Open Access
Iterative methods based on splittings for stochastic automata networks
(1998) Uysal, E.; Dayar T.
This paper presents iterative methods based on splittings (Jacobi, Gauss-Seidel, Successive Over Relaxation) and their block versions for Stochastic Automata Networks (SANs). These methods prove to be better than the power method that has been used to solve SANs until recently. With the help of three examples we show that the time it takes to solve a system modeled as a SAN is still substantial and it does not seem to be possible to solve systems with tens of millions of states on standard desktop workstations with the current state of technology. However, the SAN methodology enables one to solve much larger models than those could be solved by explicitly storing the global generator in the core of a target architecture especially if the generator is reasonably dense. © 1998 Elsevier Science B.V. All rights reserved.
Open Access
Two novel multiway circuit partitioning algorithms using relaxed locking
(IEEE, 1997) Dasdan, A.; Aykanat, Cevdet
All the previous Kernighan-Lin-based (KL-based) circuit partitioning algorithms employ the locking mechanism, which enforces each cell to move exactly once per pass. In this paper, we propose two novel approaches for multiway circuit partitioning to overcome this limitation. Our approaches allow each cell to move more than once. Our first approach still uses the locking mechanism but in a relaxed way. It introduces the phase concept such that each pass can include more than one phase, and a phase can include at most one move of each cell. Our second approach does not use the locking mechanism at all. It introduces the mobility concept such that each cell can move as freely as allowed by its mobility. Each approach leads to KL-based generic algorithms whose parameters can be set to obtain algorithms with different performance characteristics. We generated three versions of each generic algorithm and evaluated them on a subset of common benchmark circuits in comparison with Sanchis' algorithm (FMS) and the simulated annealing algorithm (SA). Experimental results show that our algorithms are efficient, they outperform FMS significantly, and they perform comparably to SA. Our algorithms perform relatively better as the number of parts in the partition increases as well as the density of the circuit decreases. This paper also provides guidelines for good parameter settings for the generic algorithms. © 1997 IEEE.