کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
394010 665714 2010 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A dynamic programming algorithm for simulation of a multi-dimensional torus in a crossed cube
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
A dynamic programming algorithm for simulation of a multi-dimensional torus in a crossed cube
چکیده انگلیسی

The torus is a popular interconnection topology and several commercial multicomputers use a torus as the basis of their communication network. Moreover, there are many parallel algorithms with torus-structured and mesh-structured task graphs have been developed. If one network can embed a mesh or torus network, the algorithms with mesh-structured or torus-structured can also be used in this network. Thus, the problem of embedding meshes or tori into networks is meaningful for parallel computing. In this paper, we prove that for n ⩾ 6 and 1 ⩽ m ⩽ ⌈n/2⌉ − 1, a family of 2m disjoint k  -dimensional tori of size 2s1×2s2×⋯×2sk2s1×2s2×⋯×2sk each can be embedded in an n-dimensional crossed cube with unit dilation, where each si ⩾ 2, ∑i=1ksi=n-m, and max1⩽i⩽k{si} ⩾ 3 if n   is odd and m=n-32; otherwise, max1⩽i⩽k{si} ⩾ n − 2m − 1. A new concept, cycle skeleton, is proposed to construct a dynamic programming algorithm for embedding a desired torus into the crossed cube. Furthermore, the time complexity of the algorithm is linear with respect to the size of desired torus. As a consequence, a family of disjoint tori can be simulated on the same crossed cube efficiently and in parallel.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Information Sciences - Volume 180, Issue 24, 15 December 2010, Pages 5090–5100
نویسندگان
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