The traveling beams optical solutions for bounded NP-complete problems

Shlomi Dolev; Hen Fitoussi

doi:10.1007/978-3-540-72914-3_12

The traveling beams optical solutions for bounded NP-complete problems

Shlomi Dolev
, Hen Fitoussi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

26 Scopus citations

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 pre-processing stage in which O(n²) 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 designs for solving Hamiltonian path, Traveling Salesman, Clique, Independent Set, Vertex Cover, Partition, 3-SAT, and 3D-matching.

Original language	English
Title of host publication	Fun with Algorithms - 4th International Conference, FUN 2007, Proceedings
Publisher	Springer Verlag
Pages	120-134
Number of pages	15
ISBN (Print)	9783540729136
DOIs	https://doi.org/10.1007/978-3-540-72914-3_12
State	Published - 1 Jan 2007
Event	4th International Conference on Fun with Algorithms, FUN 2007 - Castiglioncello, Italy Duration: 3 Jun 2007 → 5 Jun 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4475 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	4th International Conference on Fun with Algorithms, FUN 2007
Country/Territory	Italy
City	Castiglioncello
Period	3/06/07 → 5/06/07

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-540-72914-3_12

Cite this

Dolev, S., & Fitoussi, H. (2007). The traveling beams optical solutions for bounded NP-complete problems. In Fun with Algorithms - 4th International Conference, FUN 2007, Proceedings (pp. 120-134). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4475 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-72914-3_12

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title = "The traveling beams optical solutions for bounded NP-complete problems",

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 pre-processing stage in which O(n2) 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 designs for solving Hamiltonian path, Traveling Salesman, Clique, Independent Set, Vertex Cover, Partition, 3-SAT, and 3D-matching.",

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Dolev, S & Fitoussi, H 2007, The traveling beams optical solutions for bounded NP-complete problems. in Fun with Algorithms - 4th International Conference, FUN 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4475 LNCS, Springer Verlag, pp. 120-134, 4th International Conference on Fun with Algorithms, FUN 2007, Castiglioncello, Italy, 3/06/07. https://doi.org/10.1007/978-3-540-72914-3_12

The traveling beams optical solutions for bounded NP-complete problems. / Dolev, Shlomi; Fitoussi, Hen.
Fun with Algorithms - 4th International Conference, FUN 2007, Proceedings. Springer Verlag, 2007. p. 120-134 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4475 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - 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 pre-processing stage in which O(n2) 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 designs for solving Hamiltonian path, Traveling Salesman, Clique, Independent Set, Vertex Cover, Partition, 3-SAT, and 3D-matching.

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Dolev S, Fitoussi H. The traveling beams optical solutions for bounded NP-complete problems. In Fun with Algorithms - 4th International Conference, FUN 2007, Proceedings. Springer Verlag. 2007. p. 120-134. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-72914-3_12

The traveling beams optical solutions for bounded NP-complete problems

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