Abstract
This paper shows an important exception against the common perception that three-dimensional meshes are more powerful than two-dimensional ones: Let N be the total number of processors. Then permutation routing over three-dimensional mesh computers needs Θ(N 2/3) steps while it takes Θ(N 1/2) steps over two-dimensional ones under the following condition: (1) The path of each packet must be determined solely by its initial position and destination, i.e., the algorithm must be oblivious. (2) Each path must be “elementary,” i.e., it must be shortest and as straight as possible. Thus the conditions are quite reasonable in practice, under which, little surprisingly, three-dimensional meshes are significantly less powerful than two-dimensional ones for the fundamental network operation.
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© 1997 Springer-Verlag Berlin Heidelberg
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Iwama, K., Miyano, E. (1997). Three-dimensional meshes are less powerful than two-dimensional ones in oblivious routing. In: Burkard, R., Woeginger, G. (eds) Algorithms — ESA '97. ESA 1997. Lecture Notes in Computer Science, vol 1284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63397-9_22
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DOI: https://doi.org/10.1007/3-540-63397-9_22
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