Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems

Natan T. Shaked; Tal Tabib; Gil Simon; Stephane Messika; Shlomi Dolev; Joseph Rosen

doi:10.1117/1.2799086

Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems

Natan T. Shaked, Tal Tabib, Gil Simon, Stephane Messika, Shlomi Dolev, Joseph Rosen

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

An optical method for synthesizing a binary matrix representing all feasible solutions of a bounded (input length restricted) NP-complete combinatorial problem is presented. After the preparation of this matrix, an optical matrix-vector multiplier can be used in order to multiply the synthesized binary matrix and a grayscale vector representing the weights of the problem. This yields the required solution vector. The synthesis of the binary matrix is based on an efficient algorithm that utilizes a small number of long-vector duplications. These duplications are performed optically by using an optical correlator. Simulations and experimental results are given.

Original language	English
Article number	108201
Journal	Optical Engineering
Volume	46
Issue number	10
DOIs	https://doi.org/10.1117/1.2799086
State	Published - 1 Oct 2007

Keywords

Correlators
Fourier optics
Matrix multiplication
Optical computing

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics
General Engineering

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10.1117/1.2799086

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title = "Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems",

abstract = "An optical method for synthesizing a binary matrix representing all feasible solutions of a bounded (input length restricted) NP-complete combinatorial problem is presented. After the preparation of this matrix, an optical matrix-vector multiplier can be used in order to multiply the synthesized binary matrix and a grayscale vector representing the weights of the problem. This yields the required solution vector. The synthesis of the binary matrix is based on an efficient algorithm that utilizes a small number of long-vector duplications. These duplications are performed optically by using an optical correlator. Simulations and experimental results are given.",

keywords = "Correlators, Fourier optics, Matrix multiplication, Optical computing",

author = "Shaked, {Natan T.} and Tal Tabib and Gil Simon and Stephane Messika and Shlomi Dolev and Joseph Rosen",

note = "Funding Information: This research was supported by the Israel Science Foundation Grant 119 03 as well as by Intel, Deutsche Telecom, Rita Altura Trust Chair in Computer Sciences, and the Israel Ministry of Science.",

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AU - Shaked, Natan T.

AU - Tabib, Tal

AU - Simon, Gil

AU - Messika, Stephane

AU - Dolev, Shlomi

AU - Rosen, Joseph

N1 - Funding Information: This research was supported by the Israel Science Foundation Grant 119 03 as well as by Intel, Deutsche Telecom, Rita Altura Trust Chair in Computer Sciences, and the Israel Ministry of Science.

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N2 - An optical method for synthesizing a binary matrix representing all feasible solutions of a bounded (input length restricted) NP-complete combinatorial problem is presented. After the preparation of this matrix, an optical matrix-vector multiplier can be used in order to multiply the synthesized binary matrix and a grayscale vector representing the weights of the problem. This yields the required solution vector. The synthesis of the binary matrix is based on an efficient algorithm that utilizes a small number of long-vector duplications. These duplications are performed optically by using an optical correlator. Simulations and experimental results are given.

AB - An optical method for synthesizing a binary matrix representing all feasible solutions of a bounded (input length restricted) NP-complete combinatorial problem is presented. After the preparation of this matrix, an optical matrix-vector multiplier can be used in order to multiply the synthesized binary matrix and a grayscale vector representing the weights of the problem. This yields the required solution vector. The synthesis of the binary matrix is based on an efficient algorithm that utilizes a small number of long-vector duplications. These duplications are performed optically by using an optical correlator. Simulations and experimental results are given.

KW - Correlators

KW - Fourier optics

KW - Matrix multiplication

KW - Optical computing

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Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems

Abstract

Keywords

ASJC Scopus subject areas

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