Optical solution for bounded NP-complete problems

Natan T. Shaked; Stephane Messika; Shlomi Dolev; Joseph Rosen

doi:10.1364/AO.46.000711

Optical solution for bounded NP-complete problems

Natan T. Shaked, Stephane Messika, Shlomi Dolev, Joseph Rosen

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

49 Scopus citations

Abstract

We present a new optical method for solving bounded (input-length- restricted) NP-complete combinatorial problems. We have chosen to demonstrate the method with an NP-complete problem called the traveling salesman problem (TSP). The power of optics in this method is realized by using a fast matrix-vector multiplication between a binary matrix, representing all feasible TSP tours, and a gray-scale vector, representing the weights among the TSP cities. The multiplication is performed optically by using an optical correlator. To synthesize the initial binary matrix representing all feasible tours, an efficient algorithm is provided. Simulations and experimental results prove the validity of the new method.

Original language	English
Pages (from-to)	711-724
Number of pages	14
Journal	Applied Optics
Volume	46
Issue number	5
DOIs	https://doi.org/10.1364/AO.46.000711
State	Published - 10 Feb 2007

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics
Engineering (miscellaneous)
Electrical and Electronic Engineering

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AU - Messika, Stephane

AU - Dolev, Shlomi

AU - Rosen, Joseph

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AB - We present a new optical method for solving bounded (input-length- restricted) NP-complete combinatorial problems. We have chosen to demonstrate the method with an NP-complete problem called the traveling salesman problem (TSP). The power of optics in this method is realized by using a fast matrix-vector multiplication between a binary matrix, representing all feasible TSP tours, and a gray-scale vector, representing the weights among the TSP cities. The multiplication is performed optically by using an optical correlator. To synthesize the initial binary matrix representing all feasible tours, an efficient algorithm is provided. Simulations and experimental results prove the validity of the new method.

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Optical solution for bounded NP-complete problems

Abstract

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