An optical fiber network oracle for NP-complete problems

Light: Science and Applications

Volumn 3, Issue , 2014, Pages

  Wu, Kan ^a   García De Abajo, Javier ^b,c   Soci, Cesare ^a   Ping Shum, Perry ^a   Zheludev, Nikolay I ^a,b  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^c INSTITUTO DE QUÍMICA FÍSICA ROCASOLANO   (Spain)

Author keywords

Hamiltonian path problem; NP complete; optical oracle

Indexed keywords

CODES (SYMBOLS); COMPUTATIONAL COMPLEXITY; FIBERS; HAMILTONIANS; OPTICAL COMMUNICATION; OPTICAL FIBERS; PHOTONICS; POLYNOMIALS; TRAVEL TIME;

COMMUNICATION APPLICATION; HAMILTONIAN PATH PROBLEMS; INFORMATION CARRIERS; MATHEMATICAL COMPLEXITY; NP COMPLETE; OPTICAL FIBER NETWORKS; OPTICAL ORACLE; SYNAPTIC CONNECTIONS;

COMPLEX NETWORKS;

EID: 84908140905     PISSN: None     EISSN: 20477538     Source Type: Journal    
DOI: 10.1038/lsa.2014.28     Document Type: Article

References (22)

1. Karp RM. Reducibility among combinatorial problems. In: 50 Years of Integer Programming 1958-2008. Chapter 8. Berlin/Heidelberg: Springer; 2010; 219-241
2. Cook SA. The complexity of theorem-proving procedures. In: Proceedings of the Third Annual ACM Symposium on Theory of Computing. Shaker Heights, OH: ACM; 1971; 151-158
3. DorigoM, Gambardella LM. Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 1997; 1: 53-66
4. Ouyang Q, Kaplan PD, Liu S, Libchaber A. DNA solution of the maximal clique problem. Science 1997; 278: 446-449
5. Aaronson S. NP-complete problems and physical reality. SIGACT News 2005; 36: 30-52
6. Kieu T. Quantum algorithm for Hilberts tenth problem. Int J Theor Phys 2003; 42: 1461-1478
7. OBrien JL. Optical quantum computing. Science 2007; 318: 1567-1570
8. Adleman LM. Molecular computation of solutions to combinatorial problems. Science 1994; 266: 1021-1024
9. Ezziane Z. DNA computing: applications and challenges. Nanotechnology 2006; 17: R27
10. Liu Q, Wang L, Frutos AG, Condon AE, Corn RM et al. DNA computing on surfaces. Nature 2000; 403: 175-179
11. Caulfield HJ, Dolev S. Why future supercomputing requires optics. Nat Photon 2010; 4: 261-263
12. Oltean M. Solving the Hamiltonian path problem with a light-based computer. Nat Comput 2008; 7: 57-70
13. Shaked NT, Messika S, Dolev S, Rosen J. Optical solution for bounded NP-complete problems. Appl Opt 2007; 46: 711-724
14. Woods D, Naughton TJ. Optical computing: photonic neural networks. Nat Phys 2012; 8: 257-259
15. Haist T, Osten W. An optical solution for the traveling salesman problem. Opt Express 2007; 15: 10473-10482
16. Sartakhti JS, Jalili S, Rudi AG. A new light-based solution to the Hamiltonian path problem. Future Gen Comput Syst 2013; 29: 520-527
17. Dolev S, Fitoussi H. Masking traveling beams: optical solutions for NP-complete problems, trading space for time. Theor Comput Sci 2010; 411: 837-853
18. Goliaei S, Jalili S, Salimi J. Light-based solution for the dominating set problem. Appl Opt 2012; 51: 6979-6983
19. Oltean M. A light-based device for solving the Hamiltonian path problem. In: Unconventional Computation. Chapter 18. Berlin/Heidelberg: Springer; 2006; 217-227
20. HeldM, Karp R. A dynamic programming approach to sequencing problems. J Soc Ind Appl Math 1962; 10: 196-210
21. Bjorklund A. Determinant sums for undirected Hamiltonicity. Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science; 23-25 October 2010; Las Vegas, NV, USA. IEEE Computer Society: Washington, DC, USA, pp 173-182
22. Samson ZL, Horak P, MacDonald KF, Zheludev NI. Femtosecond surface plasmon pulse propagation. Opt Lett 2011; 36: 250-252