By Greg Astfalk
Masking functions on complicated structure desktops, this quantity brings jointly up-to-date models of 30 articles that initially seemed in "SIAM information" from 1990 to 1995.
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Extra resources for Applications on advanced architecture computers
Rn) satisfying the constraints $. Most applications (VLSI design, image segmentation) correspond to the following set of constraints, $1, with the weights of all nodes set to 1: — for each subset TT^ of V belonging to the partition $, the number of nodes in Ki is equal to a given value BI\ WITH the total cost of the edges going from to -KJ should be minimum WITH The graph partitioning problem under constraints $1 has been proven to be NP-complete . For our application, the mapping of parallel programs on parallel architectures, we have to consider the following set of constraints, $2: minimize the sum of communication costs between processors (total cost of the edges going from TTJ to TTJ) and the variance of the loads of the different processors (variance of cost of vertices belonging to a given TTJ): MKIN With K = 0 the set of constraints $2 reduces to 4>i.
The main inefficiency is due to the fact that since groups of 32 processors share a 32-bit Weitek floating-point chip, there is a transposer chip that changes 32 bits stored bit-serially within 32 processors into 32 32-bit words for the Weitek, and vice versa. This means that all Paris operations using the FPU must be done in chunks of 32 words. Because the internal architecture of the Weitek chips used in the CM-2 includes only 32 registers, there is no room for storing intermediate results in the Weitek.
Fortunately, there is an analytical trick whereby the quark action can be rewritten in terms of pseudofermion fields >, which are normal numbers, Thus the path integral we want to evaluate numerically is Note that the lattice is a mathematical construct used to solve the theory— at the end of the day, the lattice spacing a must be taken to zero to get back to the continuum limit. The lattice spacing itself does not show up explicitly in the partition function Z above. Instead the lattice spacing is an implicit function of the parameter (3 = 6/#2, which plays the role of an inverse temperature.