I. T. Christou, Distributed Genetic Algorithms for Partitioning Uniform Grids, University of Wisconsin Madison, Dept. of Computer Sciences Technical Report MP-TR-96-09, Madison, Wisconsin, 1996  Home/Search   Document Details and Download   Summary   Related Articles   Check

....A p (number of vertices assigned to processor p) p = 1, P, of vertices. The corresponding network problem would have P supply nodes with capacities A p , V demand nodes (note: V is used to denote V as well as the set V) each with a demand of 1, and a quadratic objective function (see [Chr96] Let, x p i = 1 if vertex i is assigned to processor p = 0 otherwise, and consider the following problem: min # i,j ( # P p,p # =1,p#=p # c ij x p i x p # j ) s.t. # # # # # # # # # # # # # # # # i#V x p i = A p p = 1, P # P p=1 x p i = 1 i # V ....

....perimeter when partitioning A cells evenly among P processors is: 2P(#2(A P) 0.5 #) All the developed methodology below is based on the geometric model. 1. 3 Motivation and Background This research is a continuation of work done by Yackel and Meyer (YM, Yac93] Christou and Meyer (CM, Chr96] and Martin [Mar98] For the partitioning of a grid graph, the methodologies of Christou and Martin [Chr96] Mar98] both outperform more wellknown algorithms such as recursive spectral bisection and geometric mesh partition (both algorithms will be described in Chapter 2) Table 1 contains ....

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I. Christou. Distributed Genetic Algorithms for Partitioning Uniform Grids. PhD thesis, University of Wisconsin - Madison, August 1996.

....number of stripes is super polynomial with respect to the number of cells in the grid, since 3 M 0.5 4 3 # 3 (no.ofcells) 0.25 4 3 From this result, we know that there are at least a super polynomial number of feasible solutions and that an exhaustive search it is not practical. In [2], an upper bound of 2 M 1 is given, but this bound allows stripes that may not contain enough cells to complete the assignment of a processor, and hence do not conform to the stripe form solutions considered here. 20 8 An Example Illustrating the Methods The example in figure 13 will be used ....

I. Christou. Distributed Genetic Algorithms for Partitioning Uniform Grids. PhD thesis, University of Wisconsin - Madison, August 1996.

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I. T. Christou, Distributed Genetic Algorithms for Partitioning Uniform Grids, University of Wisconsin Madison, Dept. of Computer Sciences Technical Report MP-TR-96-09, Madison, Wisconsin, 1996

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