Enhance Algorithm Performance Research Articles

A basic-cycle calculation technique for efficient dynamic data redistribution

Array redistribution is usually required to enhance algorithm performance in many parallel programs on distributed memory multicomputers. Since it is performed at run-time, there is a performance trade-off between the efficiency of the new data decomposition for a subsequent phase of an algorithm and the cost of redistributing data among processors. In this paper, we present a basic-cycle calculation technique to efficiently perform BLOCK-CYCLIC(S) to BLOCK-CYCLIC(t) redistribution. The main idea of the basic-cycle calculation technique is, first, to develop closed forms for computing source/destination processors of some specific array elements in a basic-cycle, which is defined as icm(s,t)/gcd(s,t). These closed forms are then used to efficiently determine the communication sets of a basic-cycle. From the source/destination processor/data sets of a basic-cycle, we can efficiently perform a BLOCK-CYCLIC(s) to BLOCK-CYCLIC(t) redistribution. To evaluate the performance of the basic-cycle calculation technique, we have implemented this technique on an IBM SP2 parallel machine, along with the PITFALLS method and the multiphase method. The cost models for these three methods are also presented. The experimental results show that the basic-cycle calculation technique outperforms the PITFALLS method and the multiphase method for most test samples.

Efficient Methods for kr → r and r → kr Array Redistribution1

Array redistribution is usually required to enhance algorithm performance in many parallel programs on distributed memory multicomputers. Since it is performed at run-time, there is a performance tradeoff between the efficiency of new data decomposition for a subsequent phase of an algorithm and the cost of redistributing data among processors. In this paper, we present efficient algorithms for BLOCK-CYCLIC(kr) to BLOCK-CYCLIC(r) and BLOCK-CYCLIC(r) to BLOCK-CYCLIC(kr) redistribution. The most significant improvement of our methods is that a processor does not need to construct the send/receive data sets for a redistribution. Based on the packing/unpacking information that derived from the BLOCK-CYCLIC(kr) to BLOCK-CYCLIC(r) redistribution and vice versa, a processor can pack/unpack array elements into (from) messages directly. To evaluate the performance of our methods, we have implemented our methods along with the Thakur‘s methods and the PITFALLS method on an IBM SP2 parallel machine. The experimental results show that our algorithms outperform the Thakur‘s methods and the PITFALLS method for all test samples. This result encourages us to use the proposed algorithms for array redistribution.

Processor mapping techniques toward efficient data redistribution

Run-time data redistribution can enhance algorithm performance in distributed-memory machines. Explicit redistribution of data can be performed between algorithm phases when a different data decomposition is expected to deliver increased performance for a subsequent phase of computation. Redistribution, however, represents increased program overhead as algorithm computation is discontinued while data are exchanged among processor memories. In this paper, we present a technique that minimizes the amount of data exchange for BLOCK to CYCLIC(c) (or vice-versa) redistributions of arbitrary number of dimensions. Preserving the semantics of the target (destination) distribution pattern, the technique manipulates the data to logical processor mapping of the target pattern. When implemented on an IBM SP, the mapping technique demonstrates redistribution performance improvements of approximately 40% over traditional data to processor mapping. Relative to the traditional mapping technique, the proposed method affords greater flexibility in specifying precisely which data elements are redistributed and which elements remain on-processor.

Global Optimization Using Interval Analysis.

Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis simplifies algorithm construction and increases generality of interval arithmetic. This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonlinear equations and global optimization problems. It expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance. Provided algorithms are guaranteed to find and bound all solutions to these problems despite bounded errors in data, in approximations, and from use of rounded arithmetic.