Abstract
We present a design for a micro optical architecture for solving instances of NP-hard problems, using nano-technology. The architecture is using pre-processed masks to block some of the light propagating through them. We demonstrate how such a device could be used to solve instances of Hamiltonian-cycle and the Permanent problems.
Partially supported by Deutsche Telekom, the ICT Programme of the European Union under contract number FP7-215270 (FRONTS), Rita Altura Trust Chair in Computer Sciences, and the Lynne and William Frankel Center for Computer Sciences. Emails: {dolev,eyalco}@cs.bgu.ac.il, rmichael@bgu.ac.il, fsergei@mail.ru, puzis@bgu.ac.il. An extended version appears as TR of the Dept. of Computer Science, BGU.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anter, A., Dolev, S.: Optical solution for hard on average #P-complete instances. Natural Computing (2010)
Cook, S.A.: The complexity of theorem-proving procedures. In: Proc. of the 3rd Ann. ACM Symp. On Theory of Computing, pp. 151–158 (1971)
Dolev, S., Fitoussi, H.: Masking traveling beams: Optical solutions for NP-complete problems, trading space for time. Theoretical Comp. Science 411, 837 (2010)
Dolev, S., Fitoussi, H.: Primitive Operations for Graph-Optical Processor. In: 6th Haifa Workshop on Interdisciplinary Applications of Graph Theory, Combinatorics, and Algorithms (May 2006)
Dolev, S., Fitoussi, H.: The Traveling Beams: Optical Solutions for Bounded NP-Complete Problems, Technical report #07-04, Ben Gurion University of the Negev (January 2007)
Dolev, S., Korach, E., Uzan, G.: A Method for Encryption and Decryption of Messages, PCT Patent Application WO 2006/001006 (January 2006)
Dolev, S., Yuval, N.: Optical implementation of bounded non-deterministic Turing machines, US Patent 7,130,093 B2, January 2005, Filed (May 2004)
Feitelson, G.: Optical Computing: A Survey for Computer Scientists. MIT Press, Cambridge (1988)
Garey, M.R., Johnson, D.S.: Computers and Intractability, a guide to the theory of NP completeness. W. H. Freeman and Company, San Francisco (1979)
Gutfreund, D., Shaltiel, R., Ta-Shma, A.: If NP Languages are Hard on the Worst-Case, then it is easy to find their Hard Instances. Journal of Computational Complexity (2007)
Haist, T., Osten, W.: An Optical Solution For The Traveling Salesman Problem. Opt. Express 15, 10473–10482 (2007)
Hopcroft, J.E., Karp, R.M.: An algorithm for maximum matching in bipartite graphs. SIAM J. Computing 2, 225–231 (1973)
Hyman, A.: Charles Babbage: Pioneer of the Computer. Princeton University Press, Princeton (1982)
Karp, R.M.: Reducibilty among combinatorial problems. Complexity of Computer Computations, 85–103 (1972)
Lenslet LTD, http://www.hpcwire.com/hpcwire/hpcwireWWW/03/1017/106185.html
Mann, H.J., Ulrich, W., Seitz, G.: 8-Mirror microlithography projection objective, US Patent 2004/0012866 A1, January 2004, Filed (April 2003)
McAulay, A.D.: Optical computer architectures. John Wiley, Chichester (1991)
Oltean, M.: A Light-Based Device for Solving the Hamiltonian Path Problem. In: Calude, C.S., Dinneen, M.J., Păun, G., Rozenberg, G., Stepney, S. (eds.) UC 2006. LNCS, vol. 4135, pp. 217–227. Springer, Heidelberg (2006)
Oltean, M., Muntean, O.: Solving the subset-sum problem with a light-based device. In: Natural Computing, Springer, Heidelberg (2007)
Shaked, N.T., Messika, S., Dolev, S., Rosen, J.: Optical solution for Bounded NP-Complete Problems. Journal of App. Optics 46, 711 (2007)
Reif, J.H., Tygar, D., Yoshida, A.: The Computability and Complexity of Optical Beam Tracing. In: 31st Annual IEEE Symposium on Foundations of Computer Science, pp. 106–114 (1990); Also The Computability and Complexity of Ray Tracing. Discrete and Computational Geometry 11, 265-287 (1994)
Tamir, D.E., Shaked, N.T., Wilson, P.J., Dolev, S.: Electro-Optical DSP of Tera Operations per Second and Beyond (Extended Abstract). In: Dolev, S., Haist, T., Oltean, M. (eds.) OSC 2008. LNCS, vol. 5172, pp. 56–69. Springer, Heidelberg (2008)
van Emde Boas, P.: Machine Models and Simulation. In: Volume, A. (ed.) Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity (A) pp. 1–66 (1990)
Woods, D.: Optical Computing and Computational Complexity. In: Calude, C.S., Dinneen, M.J., Păun, G., Rozenberg, G., Stepney, S. (eds.) UC 2006. LNCS, vol. 4135, pp. 27–40. Springer, Heidelberg (2006)
Woods, D., Gibson, J.P.: Lower Bounds on the Computational Power of an Optical Model of Computation. In: Calude, C.S., Dinneen, M.J., Păun, G., Jesús Pérez-JÃmenez, M., Rozenberg, G. (eds.) UC 2005. LNCS, vol. 3699, pp. 237–250. Springer, Heidelberg (2005); Journal version, Natural Computing 79(1), 95–108 (2008)
Xiajun, W., Zhao, X., Bermak, A., Boussaind, F.: An AER based CMOS Polarization Image Sensor with Photo-aligned Micropolarizer Array. In: Calude, C.S., Dinneen, M.J., Păun, G., Jesús Pérez-JÃmenez, M., Rozenberg, G. (eds.) UC 2005. LNCS, vol. 3699, pp. 95–108. Springer, Heidelberg (2005); Journal version. Natural Computing  7(1), 95–108 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cohen, E., Dolev, S., Frenkel, S., Puzis, R., Rosenblit, M. (2011). Nanotechnology Based Optical Solution for NP-Hard Problems. In: Dolev, S., Oltean, M. (eds) Optical Supercomputing. OSC 2010. Lecture Notes in Computer Science, vol 6748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22494-2_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-22494-2_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22493-5
Online ISBN: 978-3-642-22494-2
eBook Packages: Computer ScienceComputer Science (R0)