K. Ito and K. K. Parhi, "Determining the minimum iteration period of an algorithm, " Journal of VLSI Signal Processing, Vol.11, No.3, pp. 229-244, Dec. 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of the normalized delays, the expression for constraint time becomes the same as that for the homogeneous case. For homogeneous graphs, the minimum iteration period that can be attained by the system is known as the iteration period bound and is known to be equal to the maximum cycle mean (MCM) [16, 9]. So far, no such tight bound is known for multirate SDF graphs that does not require the costly conversion to an expanded homogeneous equivalent graph. However, some good approximations for multirate graphs have been proposed [17] Under our model, it is easy to determine an exact bound that is ....

K. Ito and K. K. Parhi, \Determining the minimum iteration period of an algorithm," Journal of VLSI Signal Processing, vol. 11, pp. 229-244, 1995.

....in the CAD of digital systems. These problems have fundamental importance to the performance analysis of discrete event systems [3] which can also model digital systems. These problems are applicable to the performance analysis of such digital systems as synchronous [23] asynchronous [4] DSP [14], or embedded real time [18] Simply put, the algorithms for these problems are essential tools to find the cycle period of a given cyclic discrete event system. Once determined, the cycle period is used to describe the behavior of the system analytically over an infinite time period. For ....

....to find the cycle period of a given cyclic discrete event system. Once determined, the cycle period is used to describe the behavior of the system analytically over an infinite time period. For instance, the algorithms for these problems are used to compute the iteration bound of a dataflow graph [14], the time separation between event occurrences in a cyclic event graph [13] and the optimal clock schedules for circuits [22] 1.2 Related work There are many algorithms proposed for both MCRP and MCMP. We give a comprehensive classification of the fastest and the most common ones in Table 1. ....

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Ito, K., and Parhi, K. K. Determining the minimum iteration period of an algorithm. J. VLSI Signal Processing 11, 3 (Dec. 1995), 229--44.

....used to model feedbacks. 3.10 Single rate versus Multi rate We also assume that the cyclic portions of the GTG are single rate whereas the acyclic portions can be multi rate. In a multi rate system, each task can have a different rate whereas in a single rate system, each task has the same rate [65]. Since there are techniques to transform a multi rate cyclic system into an equivalent single rate one, e.g. see [65] we do not lose generality with our simplifying assumption. 3.11 Related Work The GTG model builds upon many previous models in the literature. Our model is an abstraction and ....

....whereas the acyclic portions can be multi rate. In a multi rate system, each task can have a different rate whereas in a single rate system, each task has the same rate [65] Since there are techniques to transform a multi rate cyclic system into an equivalent single rate one, e.g. see [65], we do not lose generality with our simplifying assumption. 3.11 Related Work The GTG model builds upon many previous models in the literature. Our model is an abstraction and combination of these previous models for the purposes of timing analysis. We now describe these previous models. Before ....

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K. Ito and K. K. Parhi. Determining the minimum iteration period of an algorithm. J. VLSI Signal Processing, 11(3):229--44, December 1995.

.... minimum mean cycle problem has applications in finding the cycle period in an asynchronous system [1] 2] and in data flow partitioning of synchronous systems [3] the maximum mean cycle problem has applications in finding the iteration bound of a data flow graph for digital signal processing [4], and in performance analysis of synchronous, asynchronous, or mixed systems [5] There are many algorithms proposed for the minimum mean cycle problem, e.g. 1] 6] 7] 8] 9] 10] In this paper, we focus on Karp s algorithm [7] among them because of three reasons: 1) it has one of the ....

.... e.g. 1] 6] 7] 8] 9] 10] In this paper, we focus on Karp s algorithm [7] among them because of three reasons: 1) it has one of the best asymptotic running times, 2) it also works for the maximum mean cycle problem (as proved in [11] and 3) it is usually the algorithm of choice [3] [4], 5] Originally, Karp [7] gave a theorem (Karp s theorem) to characterize the minimum cycle mean in a digraph and an algorithm to compute it efficiently. Although the running time of Karp s algorithm is given in [7] as O(nm) for a strongly connected digraph with n nodes and m arcs, its actual ....

K. Ito and K. K. Parhi, "Determining the minimum iteration period of an algorithm", Journal of VLSI Signal Processing, vol. 11, no. 3, pp. 229--244, Dec. 1995.

....analysis of digital systems are numerous. Some applications are finding the cycle time of an asynchronous system [4] 19] and of a synchronous system [24] data flow partitioning of synchronous systems [17] finding the iteration bound of a data flow graph for digital signal processing [12], performance analysis, i.e. determining the minimal period or maximal throughput rate achievable, of synchronous, asynchronous, or mixed systems [25] and rate analysis of embedded systems [20] for which some additional information is given in x 6.4. Modeling these applications using the above ....

.... of the former task and the communication delay between them [20] For finding the iteration bound of a data flow graph, each event corresponds to a task in the system; the weight of an arc is equal to the execution time of its source task, and the value of the arc is equal to its delay count [12]. 1.1. Related Work There are many algorithms proposed for the maximum profit to time ratio and the maximum mean cycle problems as shown in Table I. Although most of these algorithms are originally proposed for the minimum versions of these problems, it is easy to obtain the solution for the ....

[Article contains additional citation context not shown here]

Ito, K., and Parhi, K. K. Determining the minimum iteration period of an algorithm. J. VLSI Signal Processing 11, 3 (Dec. 1995), 229--44.

.... minimum mean cycle problem has applications in finding the cycle period in an asynchronous system [1] 2] and in data flow partitioning of synchronous systems [3] the maximum mean cycle problem has applications in finding the iteration bound of a data flow graph for digital signal processing [4], in performance analysis of synchronous, asynchronous, or mixed systems [5] and in rate analysis for embedded systems [6] The application in rate analysis for embedded systems is the reason that we have become interested in the maximum mean cycle problem. We have recently proposed a framework ....

.... A more complete list is given in [7] In this paper, we focus on Karp s algorithm [8] among them because of three reasons: 1) it has one of the best asymptotic running times, 2) it also works for the maximum mean cycle problem (as proved in [12] and 3) it is usually the algorithm of choice [3] [4], 5] Originally, Karp [8] gave a theorem (Karp s theorem) to characterize the minimum cycle mean in a digraph and an algorithm to compute it efficiently. Although the running time of Karp s algorithm is given in [8] as O(nm) for a strongly connected digraph with n nodes and m arcs, its actual ....

K. Ito and K. K. Parhi, "Determining the minimum iteration period of an algorithm", J. VLSI Signal Processing, vol. 11, no. 3, pp. 229--244, Dec. 1995.

....concerning the multirate iteration bounds. A quite imprecise metric is given in [7] linear in WST ) Another approach [8] is only valid at certain points (this point is the defined CM from eq. 2) An optimized approach for the conversion to a SR DFG with removal of some redundancy is given in [14]. A typical relation of the maximum throughput vs. number of delays is presented on figure 2. We observe a huge gap between the linear limit and the maximum throughput depending of the value of WST . The more tokens we add on the arcs the more we increase WST . The throughput is monotonic over WST ....

K.Ito and K.K.Parhi, "Determining the minimum iteration period of an algorithm," Journal of VLSI Signal Processing, vol. 11, 1995.

.... focus on their applications in the performance analysis: these problems have fundamental importance to the performance analysis of discrete event systems [3] which are general enough to model the manufacturing systems [3] and digital systems such as synchronous [20] asynchronous [4] data flow [12], and embedded real time [16] systems. Simply put, the algorithms for these problems are essential tools to find the cycle period of a given cyclic discrete event system. Once determined, the cycle period is used to describe the behavior of the system analytically over an infinite time period. ....

....Name Source Year Running time Result Complexity 11 Burns Burns [4] 1991 O(n 2 m) Exact Polynomial 12 Megiddo [17] 1979 O(n 2 m lg n) Exact Polynomial 13 Hartmann Orlin [11] 1993 O(Tm) Exact Pseudopoly. 14 Lawler s Lawler [15] 1976 O(nm lg(nW ) Approximate Pseudopoly. 15 Ito Parhi [12] 1995 O(Tm T 3 ) Exact Pseudopoly. 16 Gerez et al. 9] 1992 O(Tm T 3 lg T ) Approximate Pseudopoly. 17 Gerez et al. 9] 1992 O(Tm T 4 ) Exact Pseudopoly. 18 Howard s Cochet Terrasson et al. 6] 1997 O(Nm) Exact Pseudopoly. one algorithm. The notation W is the largest integer arc weight, T ....

Ito, K., and Parhi, K. K. Determining the minimum iteration period of an algorithm. J. VLSI Signal Processing 11, 3 (Dec. 1995), 229--44.

....longer than the iteration lower bound, any schedule in the non overlapped manner cannot achieve the iteration lower bound. Only the overlapped schedule can always achieve the iteration lower bound. The technique to compute the iteration lower bound for a given processing algorithm can be found in [9] [12] Fig. 3(a) shows a schedule of some processing algorithm. The duration to execute every operation in the processing algorithm once is longer than the iteration period T . 4 IEICE TRANS. FUNDAMENTALS, VOL. E00 A, NO. 3 MARCH 1998 Operations a and b are scheduled to start at time steps J ....

K. Ito and K. K. Parhi, "Determining the Minimum Iteration Period of an Algorithm," Journal of VLSI Signal Processing, vol. 11, pp. 229--244, Dec. 1995.

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K. Ito and K. K. Parhi, "Determining the minimum iteration period of an algorithm, " Journal of VLSI Signal Processing, Vol.11, No.3, pp. 229-244, Dec. 1995.

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