Skip to main content
SpringerLink
Log in

Exact Cover with Light

  • Published:
New Generation Computing Aims and scope Submit manuscript

Abstract

We suggest a new optical solution for solving the YES/NO version of the Exact Cover problem by using the massive parallelism of light. The idea is to build an optical device which can generate all possible solutions of the problem and then to pick the correct one. In our case the device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. The nodes are connected by arcs in a special way which lets us to generate all possible covers (exact or not) of the given set. For selecting the correct solution we assign to each item, from the set to be covered, a special integer number. These numbers will actually represent delays induced to light when it passes through arcs. The solution is represented as a subray arriving at a certain moment in the destination node. This will tell us if an exact cover does exist or not.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Adleman, L., “Molecular computation of solutions to combinatorial problems,” Science Vol. 266, pp. 1021–1024, 1994.

    Article  Google Scholar 

  2. Agrawal G.P. (2002). Fiber-optic communication systems. Wiley-Interscience (3rd Edition), 2002.

  3. Bajcsy, M., Zibrov, A.S. and Lukin, M.D., “Stationary pulses of light in an atomic medium,” Nature, Vol. 426, pp. 638–641, 2003.

    Article  Google Scholar 

  4. Cormen, T.H., Leiserson, C.E. and Rivest, R.R., Introduction to algorithms (Second Edition), MIT Press, 2001.

  5. Collings, N., Sumi, R., Weible, K.J., Acklin, B. and Xue, W., “The use of optical hardware to find good solutions of the travelling salesman problem (TSP),” in Proc. SPIE 1806, pp. 637–641, 1993.

  6. Desurvire, E., Simpson. J. and Becker, P.C., “High-gain erbium-doped travelingwave fiber amplifier” Optics Letters, Vol. 12, No. 11, pp. 888–890, 1987.

    Article  Google Scholar 

  7. Faist, J., “Optoelectronics: silicon shines on,” Nature, Vol. 433, pp. 691–692, 2005.

    Article  Google Scholar 

  8. Flyckt, S.O. and Marmonier, C., Photomultiplier tubes: Principles and applications. Photonis, Brive, France, 2002.

    Google Scholar 

  9. Garey, M.R. and Johnson, D.S., Computers and intractability: A guide to NPCompleteness, Freeman & Co, San Francisco, CA, 1979.

    Google Scholar 

  10. Goodman, J.W., “Architectural development of optical data processing systems,” Aust. J. Electr. Electron. Eng, Vol. 2, pp. 139–149, 1982.

    Google Scholar 

  11. Haist, T. and Osten, W., “An Optical Solution For The Traveling Salesman Problem,” Opt. Express, Vol. 15, pp. 10473–10482, 2007.

    Article  Google Scholar 

  12. Hardy, J. and Shamir, J., “Optics inspired logic architecture,” Opt. Express, Vol. 15, pp. 150–165, 2007.

    Article  Google Scholar 

  13. Hartmanis, J., “On the weight of computations,” Bulletin of the EATCS, Vol. 55, pp. 136–138, 1995.

    MATH  Google Scholar 

  14. Hau, L.V., Harris, S.E., Dutton, Z. and Behroozi, C.H., “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature, Vol. 397, pp. 594–598, 1999.

    Article  Google Scholar 

  15. Henkel, C., Frisco, P. and Tengely, S.Z., “An algorithm for SAT without an extraction phase,” in DNA Computing, Eleventh International Meeting on DNA Based Computers, LNCS 3892, pp. 67–80, 2005.

  16. Lenslet website, www.lenslet.com, 2005.

  17. Liu. C., Dutton, Z., Behroozi, C.H. and Hau, L.V., “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature, Vol. 409, pp. 490–493, 2001.

    Article  Google Scholar 

  18. Mears. R.J,, Reekie. L., Jauncey, I.M., and Payne, D.N., “Low-noise Erbiumdoped fibre amplifier at 1.54pm,” Electron. Lett., Vol. 23, pp. 1026–1028, 1987.

    Article  Google Scholar 

  19. Murphy, N., Naughton, T.J., Woods, D., Henley, B., McDermott, K., Duffy, E., van der Burgt, P.J.M. and Woods, N., “Implementations of a model of physical sorting,” in From Utopian to Genuine Unconventional Computers workshop(Adamatzky A, Teuscher C, eds.), Luniver Press pp. 79–100, 2006.

  20. Naughton, T.J., “A model of computation for Fourier optical processors,” in Optics in Computing (Lessard R.A, Galstian T eds.), Proc. SPIE 4089, pp. 24–34, 2000.

  21. Oltean, M., “A light-based device for solving the Hamiltonian path problem,” Unconventional Computing (Calude C. et al. eds.), LNCS 4135, Springer-Verlag, pp. 217–227, 2006.

  22. Oltean, M., “Solving the Hamiltonian path problem with a light-based computer,” Natural Computing, Vol.7-1, pp.57–70, Springer-Verlag, 2008.

  23. Paniccia, M. and Koehl, S., “The silicon solution,” IEEE Spectrum, IEEE Press, October, 2005.

  24. Pisinger, D., “Dynamic Programming on the word RAM,”Algorithmica, Vol. 35, pp. 128–145, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  25. Rader, A. and Anderson, B.L., “Demonstration of a Linear Optical True-Time Delay Device by Use of a Microelectromechanical Mirror Array,” Applied Optics, Vol. 42, pp. 1409–1416, 2003.

    Article  Google Scholar 

  26. Reif, J.H. and Tyagi, A., “Efficient parallel algorithms for optical computing with the discrete Fourier transform primitive,” Applied optics, Vol. 36(29), pp. 7327–7340, 1987.

    Article  Google Scholar 

  27. Rong, H., Jones, R., Liu, A., Cohen, O., Hak, D., Fang, A. and Paniccia, M., “A continuous-wave Raman silicon laser,” Nature, Vol. 433, pp. 725–728, 2005.

    Article  Google Scholar 

  28. Rong, H., Liu, A., Jones, R., Cohen, O., Hak, D., Nicolaescu, R., Fang, A. and Paniccia, M., “An all-silicon Raman laser,” Nature, Vol. 433, pp. 292–294, 2005.

    Article  Google Scholar 

  29. Schultes, D., “Rainbow Sort: Sorting at the speed of light,” Natural Computing, Vol. 5(1), Springer-Verlag, pp. 67–82, 2005.

  30. Shaked, N.T., Messika, S., Dolev, S. and Rosen, J., “Optical solution for bounded NP-complete problems,” Applied Optics, Vol. 46, pp. 711–724, 2007.

    Article  Google Scholar 

  31. Sloane, N., “The on-line encyclopedia of integer sequences” http://www:research.att.com/~njas/sequences/A023758, 2006.

  32. Vergis, A., Steiglitz, K. and Dickinson, B., “The complexity of analog computation,” Mathematics and Computers in Simulation, Vol. 28(2), pp. 91–113, 1986.

    Article  MATH  Google Scholar 

  33. Woods, D., Naughton, T.J., “An optical model of computation,” Theoretical Computer Science, Vol. 334 (1-3), pp. 227–258, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  34. Optical Character Recognition @ Wikipedia, http://en.wikipedia.org/wiki/Optical_character_recognition, 2006.

  35. List of refractive indices @ Wikipedia, http://en.wikipedia.org/wiki/List_of_refractive_indices, 2007.

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Kogălniceanu 1, Cluj-Napoca, 400084, Romania

    Mihai Oltean & Oana Muntean

Authors
  1. Mihai Oltean
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Oana Muntean
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mihai Oltean.

About this article

Cite this article

Oltean, M., Muntean, O. Exact Cover with Light. New Gener. Comput. 26, 329–346 (2008). https://doi.org/10.1007/s00354-008-0049-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00354-008-0049-5

Keywords:

Search

Navigation