Bougeret, Marin and Boudet, Vincent and Dokka Venkata Satyanaraya, Trivikram and Duvillié, Guillerme and Giroudeau, Rodolphe (2016) On the complexity of Wafer-to-Wafer Integration. Discrete Optimization. ISSN 1572-5286
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Abstract
In this paper we consider the Wafer-to-Wafer Integration problem. A wafer can be seen as a pp-dimensional binary vector. The input of this problem is described by mm multisets (called “lots”), where each multiset contains nn wafers. The output of the problem is a set of nn disjoint stacks, where a stack is a set of mm wafers (one wafer from each lot). To each stack we associate a pp-dimensional binary vector corresponding to the bit-wise AND operation of the wafers of the stack. The objective is to maximize the total number of “1” in the nn stacks. We provide m1−ϵm1−ϵ and p1−ϵp1−ϵ non-approximability results even for n=2n=2, f(n)f(n) non-approximability for any polynomial-time computable function ff, as well as a View the MathML sourcepr-approximation algorithm for any constant rr. Finally, we show that the problem is View the MathML sourceFPT when parameterized by pp, and we use this View the MathML sourceFPT algorithm to improve the running time of the View the MathML sourcepr-approximation algorithm.