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    Rights statement: This is the author’s version of a work that was accepted for publication in Discrete Optimization. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Optimization, ???, ?, 2016 DOI: 10.1016/j.disopt.2016.07.001

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On the complexity of Wafer-to-Wafer Integration

Research output: Contribution to journalJournal article

E-pub ahead of print
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<mark>Journal publication date</mark>29/07/2016
<mark>Journal</mark>Discrete Optimization
Publication statusE-pub ahead of print
Early online date29/07/16
Original languageEnglish

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.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Discrete Optimization. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Optimization, ???, ?, 2016 DOI: 10.1016/j.disopt.2016.07.001