Mapping Powerlists onto Hypercubes
نویسنده
چکیده
The theory of powerlists was recently introduced by Jay Misra. It gives us the ability to specify and verify certain parallel algorithms and connection structures. The notation is similar to sequential functional programming languages (such as Miranda TM Tur86]) but with constructs for expressing balanced division of lists. In the rst part of this work we study how some known algorithms for the hypercube can be speciied succinctly in the powerlist notation. These speciications can then be veriied quite succinctly in comparison to the original proofs of the algorithms. The second part of this work is to study how algorithms written in the powerlist notation can be mapped eeciently onto the hypercube. It turns out that many algorithms have a mapping to the hypercube that is as eecient as mappings to architectures that have all to all connections. This mapping is known in the literature as the Gray code. Operators on these Gray coded powerlists can be implemented eeciently on a hyper-cube. Algebraically the Gray coding is an isomorphism between powerlists expressions and their Gray coded equivalents. 0 Introduction In the eld of parallel algorithm research most papers focus on improving the previously best known results in terms of either time{complexity or parallel work (parallel time multiplied by number of processors utilized).
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تاریخ انتشار 2010