Duvillié, Guillerme and Bougeret, Marin and Boudet, Vincent and Dokka Venkata Satyanaraya, Trivikram and Girodeau, Rodolpe
(2015)
*On the complexity of wafer-to-wafer integration.*
In:
Algorithms and Complexity.
Lecture Notes in Computer Science
.
Springer, Cham, pp. 208-220.
ISBN 9783319181721

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## Abstract

In this paper we consider the Wafer-to-Wafer Integration problem. A wafer is a p -dimensional binary vector. The input of this problem is described by m disjoints sets (called “lots”), where each set contains n wafers. The output of the problem is a set of n disjoint stacks, where a stack is a set of m wafers (one wafer from each lot). To each stack we associate a p -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 n stacks. We provide O(m 1−ϵ ) and O(p 1−ϵ ) non-approximability results even for n=2 , as well as a pr -approximation algorithm for any constant r . Finally, we show that the problem is FPT when parameterized by p , and we use this FPT algorithm to improve the running time of the pr -approximation algorithm.