In recent years, there has been considerable interest in collaborative tagging. This paper proposes a hybrid fuzzy clustering method for collaborative tagging. Key feature of the method includes using a combination of the fuzzy c-means and the subtractive clustering to handle collaborative tagging problems. The method allows a resource to belong to more than one taggings with different membership grade. The HFCT method need not know in advance the number of taggings, in order to avoid the difficulty of initial guesses of the number of taggings.

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In loops, some arrays are referenced with induction variables. To parallelize such kind of loops, those induction variables should be substituted. Thus, those array references that were substituted are formulated as nonlinear expressions. The goal of data alignment is to intelligently map the computations and data onto a set Communication-free data alignment for arrays with exponential references 5 of virtual processors which are organized as a Cartesian grid (or a template in HPF terms), and to provide data locality for parallelizing compilers so that data access communication costs can be minimized. Most data alignment methods are mainly devised to align the referenced arrays using linear subscripts or quadratic subscripts with n loop index variables, and the methods are well developed. Seldom work, however, is researched on the nonlinear expressions of index variables. This paper proposes a new communication-free data alignment technique to align the referenced arrays using exponential subscripts with n loop index variables or other complex nonlinear expressions. The experimental results using SPEC95FP Benchmarks point out that the techniques proposed in the paper can improve the execution time of the subroutines in these benchmarks.

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