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On the complexity of Wafer-to-Wafer Integration

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Title: On the complexity of Wafer-to-Wafer Integration
Authors: Duvillié, Guillerme, Bougeret, Marin, Boudet, Vincent, Dokka, Trivikram, Giroudeau, Rodolphe
Contributors: Methods, Algorithms for Operations REsearch (MAORE), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Operations Research and Business Statistics (ORSTAT), Catholic University of Leuven = Katholieke Universiteit Leuven (KU Leuven), LIRMM
Source: https://hal-lirmm.ccsd.cnrs.fr/lirmm-01110027 ; [Research Report] LIRMM. 2015.
Publisher Information: CCSD
Publication Year: 2015
Collection: LIRMM: HAL (Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier)
Subject Terms: ILP, FPT, Approximability, Wafer-to-Wafer Integration, Operational Research, Complexity & approximation, Complexity, [INFO.INFO-RO]Computer Science [cs]/Operations Research [math.OC], [INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC]
Description: 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−) and O(p 1−) non-approximability results even for n = 2, as well as a p r -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 p r -approximation algorithm.
Document Type: report
Language: English
Availability: https://hal-lirmm.ccsd.cnrs.fr/lirmm-01110027
https://hal-lirmm.ccsd.cnrs.fr/lirmm-01110027v1/document
https://hal-lirmm.ccsd.cnrs.fr/lirmm-01110027v1/file/main.pdf
Rights: https://about.hal.science/hal-authorisation-v1/ ; info:eu-repo/semantics/OpenAccess
Accession Number: edsbas.B223B24F
Database: BASE
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  – Url: https://hal-lirmm.ccsd.cnrs.fr/lirmm-01110027#
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  Data: On the complexity of Wafer-to-Wafer Integration
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  Data: <searchLink fieldCode="AR" term="%22Duvillié%2C+Guillerme%22">Duvillié, Guillerme</searchLink><br /><searchLink fieldCode="AR" term="%22Bougeret%2C+Marin%22">Bougeret, Marin</searchLink><br /><searchLink fieldCode="AR" term="%22Boudet%2C+Vincent%22">Boudet, Vincent</searchLink><br /><searchLink fieldCode="AR" term="%22Dokka%2C+Trivikram%22">Dokka, Trivikram</searchLink><br /><searchLink fieldCode="AR" term="%22Giroudeau%2C+Rodolphe%22">Giroudeau, Rodolphe</searchLink>
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  Data: Methods, Algorithms for Operations REsearch (MAORE)<br />Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM)<br />Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)<br />Operations Research and Business Statistics (ORSTAT)<br />Catholic University of Leuven = Katholieke Universiteit Leuven (KU Leuven)<br />LIRMM
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  Data: <i>https://hal-lirmm.ccsd.cnrs.fr/lirmm-01110027 ; [Research Report] LIRMM. 2015</i>.
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  Data: 2015
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  Data: <searchLink fieldCode="DE" term="%22ILP%22">ILP</searchLink><br /><searchLink fieldCode="DE" term="%22FPT%22">FPT</searchLink><br /><searchLink fieldCode="DE" term="%22Approximability%22">Approximability</searchLink><br /><searchLink fieldCode="DE" term="%22Wafer-to-Wafer+Integration%22">Wafer-to-Wafer Integration</searchLink><br /><searchLink fieldCode="DE" term="%22Operational+Research%22">Operational Research</searchLink><br /><searchLink fieldCode="DE" term="%22Complexity+%26+approximation%22">Complexity & approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Complexity%22">Complexity</searchLink><br /><searchLink fieldCode="DE" term="%22[INFO%2EINFO-RO]Computer+Science+[cs]%2FOperations+Research+[math%2EOC]%22">[INFO.INFO-RO]Computer Science [cs]/Operations Research [math.OC]</searchLink><br /><searchLink fieldCode="DE" term="%22[INFO%2EINFO-CC]Computer+Science+[cs]%2FComputational+Complexity+[cs%2ECC]%22">[INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC]</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: 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−) and O(p 1−) non-approximability results even for n = 2, as well as a p r -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 p r -approximation algorithm.
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  Data: https://hal-lirmm.ccsd.cnrs.fr/lirmm-01110027<br />https://hal-lirmm.ccsd.cnrs.fr/lirmm-01110027v1/document<br />https://hal-lirmm.ccsd.cnrs.fr/lirmm-01110027v1/file/main.pdf
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      – Text: English
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      – SubjectFull: ILP
        Type: general
      – SubjectFull: FPT
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      – SubjectFull: Approximability
        Type: general
      – SubjectFull: Wafer-to-Wafer Integration
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      – SubjectFull: Complexity & approximation
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