Natural Computing

, Volume 8, Issue 2, pp 321–331 | Cite as

Solving the subset-sum problem with a light-based device



We propose an optical computational device which uses light rays for solving the subset-sum problem. 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 subsets of the given set. To each arc we assign either a number from the given set or a predefined constant. When the light is passing through an arc it is delayed by the amount of time indicated by the number placed in that arc. At the destination node we will check if there is a ray whose total delay is equal to the target value of the subset sum problem (plus some constants). The proposed optical solution solves a NP-complete problem in time proportional with the target sum, but requires an exponential amount of energy.


Unconventional computing Optical solutions NP-complete Subset sum 


  1. Aaronson S (2005) NP-complete problems and physical reality, ACM SIGACT News Complexity Theory Column, March. ECCC TR05-026, quant-ph/0502072Google Scholar
  2. Adleman L (1994) Molecular computation of solutions to combinatorial problems. Science 266:1021–1024CrossRefGoogle Scholar
  3. Agrawal GP (2002) Fiber-optic communication systems, 3rd edn. Wiley-InterscienceGoogle Scholar
  4. Bajcsy M, Zibrov AS, Lukin MD (2003) Stationary pulses of light in an atomic medium. Nature 426:638–641CrossRefGoogle Scholar
  5. Bringsjord S, Taylor J (2004) P = NP, cs.CC/0406056Google Scholar
  6. Cormen TH, Leiserson CE, Rivest RR (1990) Introduction to algorithms. MIT PressGoogle Scholar
  7. Faist J (2005) Optoelectronics: silicon shines on. Nature 433:691–692CrossRefGoogle Scholar
  8. Feitelson DG (1988) Optical computing: a survey for computer scientists, MIT PressGoogle Scholar
  9. Flyckt SO, Marmonier C (2002) Photomultiplier tubes: principles and applications. Photonis, Brive, FranceGoogle Scholar
  10. Garey MR, Johnson DS (1979) Computers and intractability: a guide to NP-completeness. Freeman & Co, San Francisco, CAMATHGoogle Scholar
  11. Gilmore PC, Gomory RE (1965) Multistage cutting stock problems of two and more dimensions. Oper Res 13(1):94–120MATHCrossRefGoogle Scholar
  12. Goodman JW (1982) Architectural development of optical data processing systems. Aust J Electr Electron Eng 2:139–149Google Scholar
  13. Haist T and Osten W (2007) An optical solution for the traveling salesman problem. Opt Express 15:10473–10482CrossRefGoogle Scholar
  14. Hartmanis J (1995) On the weight of computations. B EATCS 55:136–138MATHGoogle Scholar
  15. Hau LV, Harris SE, Dutton Z, Behroozi CH (1999) Light speed reduction to 17 m per second in an ultracold atomic gas. Nature 397:594–598CrossRefGoogle Scholar
  16. Kieu TD (2003) Quantum algorithm for Hilbert’s tenth problem. Int J Theor Phys 42:1461–1478MATHCrossRefMathSciNetGoogle Scholar
  17. Lenslet website (2005)
  18. Liu C, Dutton Z, Behroozi CH, Hau LV (2001) Observation of coherent optical information storage in an atomic medium using halted light pulses. Nature 409:490–493CrossRefGoogle Scholar
  19. Murphy N, Naughton TJ, Woods D, Henley B, McDermott K, Duffy E, van der Burgt PJM, Woods N (2006) Implementations of a model of physical sorting. In: Adamatzky A, Teuscher C (eds) From Utopian to genuine unconventional computers workshop, Luniver Press, pp 79–100Google Scholar
  20. Naughton TJ (2000) A model of computation for Fourier optical processors. In: Lessard RA, Galstian T (eds) Optics in computing, Proceedings SPIE 4089:24–34Google Scholar
  21. Oltean M (2006) A light-based device for solving the Hamiltonian path problem. In: Calude C et al (eds) Unconventional computing LNCS 4135, Springer-Verlag, pp 217–227Google Scholar
  22. Oltean M (2007) Solving the Hamiltonian path problem with a light-based computer. Nat Comput doi:10.1007/s11047-007-9042-z
  23. Paniccia M, Koehl S (2005) The silicon solution. IEEE Spectrum, IEEE Press, OctoberGoogle Scholar
  24. Reif JH, Tyagi A (1997) Efficient parallel algorithms for optical computing with the discrete Fourier transform primitive. Appl Optics 36(29):7327–7340CrossRefGoogle Scholar
  25. Rong H, Jones R, Liu A, Cohen O, Hak D, Fang A, Paniccia M (2005a) A continuous-wave Raman silicon laser. Nature 433:725–728CrossRefGoogle Scholar
  26. Rong H, Liu A, Jones R, Cohen O, Hak D, Nicolaescu R, Fang A, Paniccia M (2005b) An all-silicon Raman laser. Nature 433:292–294CrossRefGoogle Scholar
  27. Schultes D (2005) Rainbow Sort: sorting at the speed of light. Nat Comput, Springer-Verlag 5(1):67–82Google Scholar
  28. Shaked NT, Messika S, Dolev S and Rosen J (2007) Optical solution for bounded NP-complete problems. Appl Optics 46:711–724CrossRefGoogle Scholar
  29. Shor P (1997) Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J Comput 26(5):1484–1509MATHCrossRefMathSciNetGoogle Scholar
  30. Thoughts on the subset sum problem (P vs. NP) (accessed 2006)
  31. Vergis A, Steiglitz K, Dickinson B (1986) The complexity of analog computation. Math Comput Simulat 28:91–113MATHCrossRefGoogle Scholar
  32. Woods D, Naughton TJ (2005) An optical model of computation. Theor Comput Sci 334 (1–3):227–258MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Computer Science, Faculty of Mathematics and Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania

Personalised recommendations