A Polynomial-Time Dependence Test for Determining Integer-Valued Solutions in Multi-Dimensional Arrays Under Variable Bounds

Authors:
Weng-Long Chang;Chih-Ping Chu;Jia-Hwa Wu
Affiliations:
Department of Information Management, Southern Taiwan University of Technology, Tainan County, Republic of China 710;Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Republic of China 701;Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Republic of China 701
Venue:
The Journal of Supercomputing
Year:
2005

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Abstract

Multi-dimensional arrays with linear subscripts occur quite frequently in real programs. For multi-dimensional linear arrays under variable bounds as well as any given direction vectors, the generalized Lambda test is an efficient and precise data dependence method to check whether there exist real-valued solutions. In this paper, we propose a multi-dimensional generalized interval test--a polynomial-time dependence test that can be applied towards testing whether there are integer-valued solutions for multi-dimensional linear arrays under variablelimits and any given direction vectors. Experimental results with benchmark showing the effects of the multi-dimensional generalized interval test over the generalized Lambda test are also presented.