Characterizing Data Dependence Constraints for Dynamic Reliability Using N-Queens Attack Domains
نویسندگان
چکیده
As data centers attempt to cope with the exponential growth of data, new techniques for intelligent, software-defined data centers (SDDC) are being developed to confront the scale and pace of changing resources and requirements. For costconstrained environments, like those increasingly present in scientific research labs, SDDCs also may provide better reliability and performability with no additional hardware through the use of dynamic syndrome allocation. To do so, the middleware layers of SDDCs must be able to calculate and account for complex dependence relationships to determine an optimal data layout. This challenge is exacerbated by the growth of constraints on the dependence problem when available resources are both large (due to a higher number of syndromes that can be stored) and small (due to the lack of available space for syndrome allocation). We present a quantitative method for characterizing these challenges using an analysis of attack domains for high-dimension variants of the n-queens problem that enables performable solutions via the SMT solver Z3. We demonstrate correctness of our technique, and provide experimental evidence of its efficacy; our implementation is publicly available. 2012 ACM Subject Classification Embedded and cyber-physical systems, Data centers, Theorem proving and SAT solving
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The n-queens problem in higher dimensions
The 8-queens problem is a well-known chessboard problem, whose constraints are to place eight queens on a normal chessboard in such a way that no two attack each other, under the rule that a chess queen can attack other pieces in the same column, row, or diagonal. This problem can be generalized to place n queens on an n by n chessboard, otherwise known as the n-queens problem. The mathematicia...
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