## The traveling beam: optical solution for bounded NP-complete problems (2007)

Venue: | The fourth international conference on fun with algorithms (FUN |

Citations: | 6 - 3 self |

### BibTeX

@INPROCEEDINGS{Dolev07thetraveling,

author = {Shlomi Dolev and Hen Fitoussi},

title = {The traveling beam: optical solution for bounded NP-complete problems},

booktitle = {The fourth international conference on fun with algorithms (FUN},

year = {2007},

pages = {120--134}

}

### OpenURL

### Abstract

Architectures for optical processors designed to solve bounded instances of NP-Complete problems are suggested. One approach mimics the traveling salesman by traveling beams that simultaneously examine the different possible paths. The other approach uses a preprocessing stage in which O(n 2) masks are constructed, each representing a different edge in the graph. The choice and combination of the appropriate (small) subset of these masks yields the solution. The solution is rejected in cases where the combination of these masks totally blocks the light and accepted otherwise. We present detailed designs for basic primitives of the optical processor. We propose

### Citations

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Citation Context ...ibly split) from its creation until its final detection of arrival. We extend the design for the TSP primitive suggested in [1] and present a design for all (six) basic NP-Complete problems listed in =-=[4]-=-: Hamiltonian Path, Clique, Vertex Cover, Partition, 3-SAT, and 3D-matching. Note that polynomial reduction between NP-complete Problems is not used here, since we are concerned with a constant blowup... |

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Citation Context ...a Trust Chair in Computer Science. 1sis to implement optical logic gates, such as logical and gate and logical or gate, a design that directly maps the current VLSI design to an all optical processor =-=[3, 8]-=-. On the other hand, electronic computers are not structured as mechanical computers, such as the Babbage machine [5], and it is possible that optical computers should be designed differently as well.... |

30 | Factoring large numbers with the TWINKLE device
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Citation Context ...o believe that our new designs will be used in practice for solving combinatorial tasks, at least when there are real-time constraints. Some cryptographic usage of optical processors are suggested in =-=[2, 12, 13]-=-. We would like to remark that most of our designs solve in fact the #P version of the problem. At last, we view our work as a beginning for (having fun in) further investigations on using beams of li... |

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Citation Context ...a Trust Chair in Computer Science. 1sis to implement optical logic gates, such as logical and gate and logical or gate, a design that directly maps the current VLSI design to an all optical processor =-=[3, 8]-=-. On the other hand, electronic computers are not structured as mechanical computers, such as the Babbage machine [5], and it is possible that optical computers should be designed differently as well.... |

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Citation Context ...a design that directly maps the current VLSI design to an all optical processor [3, 8]. On the other hand, electronic computers are not structured as mechanical computers, such as the Babbage machine =-=[5]-=-, and it is possible that optical computers should be designed differently as well. In fact, some success in using many beams in free space for computing has been recently reported [7]. The design of ... |

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Citation Context ...on of beams is in approximately the same direction. The beam traversal time is not used in the architectures that use Multiplication; we propose to use the time dimension as well. The seminal work of =-=[10]-=- demonstrates the mapping between beam propagation and the computation of the deterministic Turing machine. In [1] use of a mapping similar to the nondeterministic Turing machine by (amplifying and) s... |

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Citation Context ... extreme - having a very large number of cores that are incorporated into the processing by sending signals over high-speed buses, maybe using optical/laser communication instead of traditional buses =-=[9]-=-. Optical communication maybe chosen due to the free space transmission capabilities of laser beams or the need to transmit signals from/to the processing unit through fiber optic channels. In such ca... |

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Citation Context ...o believe that our new designs will be used in practice for solving combinatorial tasks, at least when there are real-time constraints. Some cryptographic usage of optical processors are suggested in =-=[2, 12, 13]-=-. We would like to remark that most of our designs solve in fact the #P version of the problem. At last, we view our work as a beginning for (having fun in) further investigations on using beams of li... |

6 |
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Citation Context ...se Multiplication; we propose to use the time dimension as well. The seminal work of [10] demonstrates the mapping between beam propagation and the computation of the deterministic Turing machine. In =-=[1]-=- use of a mapping similar to the nondeterministic Turing machine by (amplifying and) splitting beams is suggested. The mapping can be viewed as a theoretical existence proof for a solution, rather tha... |

2 |
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Citation Context ...o believe that our new designs will be used in practice for solving combinatorial tasks, at least when there are real-time constraints. Some cryptographic usage of optical processors are suggested in =-=[2, 12, 13]-=-. We would like to remark that most of our designs solve in fact the #P version of the problem. At last, we view our work as a beginning for (having fun in) further investigations on using beams of li... |

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Citation Context ... Clique, Independent Set, Vertex Cover, Partition, 3-SAT, and 3D-matching. Keywords: Optical computing, NP-Complete problems 1 Introduction The basic element used for computing is a switching element =-=[6]-=-. One such basic element in the scope of electronic circuitry is the transistor that is used to implement basic logic gates, such as logical and and logical or. The technology today seeks multi-core s... |

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Citation Context ...omputing has been recently reported [7]. The design of [7] is based on parallel optical multiplication. The use of similar multiplication devices to solve bounded NP-Complete problems is suggested in =-=[11]-=-. Still, use of the fact that beams propagate in three dimensions is limited in the multiplication architectures of [7, 11] as the propagation of beams is in approximately the same direction. The beam... |