Skip to main content
Log in

Solving jigsaw puzzles by computer

  • Published:
Annals of Operations Research Aims and scope Submit manuscript


An algorithm to assemble large jigsaw puzzles using curve matching and combinatorial optimization techniques is presented. The pieces are photographed one by one and then the assembly algorithm, which uses only the puzzle piece shape information, is applied. The algorithm was experimented successfully in the assembly of 104-piece puzzles with many almost similar pieces. It was also extended to solve an intermixed puzzle assembly problem and has successfully solved a 208-piece puzzle consisting of two intermixed 104-piece puzzles. Previous results solved puzzles with about 10 pieces, which were substantially different in shape.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others


  1. M. Belmore and J.C. Malone, Pathology of traveling-salesman subtour-elimination algorithms, Oper. Res. 19(1971)278.

    Google Scholar 

  2. M. Belmore and G.L. Nemhauser, The traveling-salesman problem: A survey, Oper. Res. 16(1968)538.

    Google Scholar 

  3. G. Burdea and H. Wolfson, Automated assembly of a jigsaw puzzle using the IBM 7565 Robot, Tech. Rep. No. 188, Comp. Sci. Div., Courant Inst. of Math., NYU (1985).

  4. N. Christofides,Graph Theory (Academic Press, 1975).

  5. Z. Fencl, Routing problem, CACM Algorithm 456.

  6. H. Freeman and L. Garder, Apictorial jigsaw puzzles: The computer solution of a problem in pattern recognition, IEEE Trans. on Electronic Comp. EC-13, 2(1964)118.

    Google Scholar 

  7. M.R. Garey and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman and Co., 1979).

  8. A. Kalvin, E. Schonberg, J.T. Schwartz and M. Sharir, Two dimensional model based boundary matching using footprints, Tech. Rep. No. 162, Comp. Sci. Div., Courant Inst. of Math., NYU (1985).

  9. E.L. Lawler,Combinatorial Optimization: Networks and Matroids (Holt, Rinehart and Winston, 1976).

  10. E.L. Lawler, J.R. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys,The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization (Wiley, 1985).

  11. T.C. Raymond, Heuristic algorithm for the traveling-salesman problem, IBM J. Res. Develop. 13, 4(1969)400.

    Google Scholar 

  12. G.M. Radack and N.I. Badler, Jigsaw puzzle matching using a boundary-centered polar encoding, Computer Graphics and Image Processing 19(1982)1.

    Google Scholar 

  13. J.T. Schwartz and M. Sharir, Identification of partially obscured objects in two dimensions by matching of noisy “characteristic curves”, Tech. Rep. No. 165, Comp. Sci. Div., Courant Inst. of Math., NYU (1985).

  14. H. Wolfson, On curve matching, Tech. Rep. No. 256, Comp. Sci. Div., Courant Inst. of Math., NYU (1986).

Download references

Author information

Authors and Affiliations


Additional information

Work on this paper has been supported by Office of Naval Research Grant N00014-82-K-0381, National Science Foundation Grant No. NSF-DCR-83-20085, and by grants from the Digital Equipment Corporation, and the IBM Corporation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wolfson, H., Schonberg, E., Kalvin, A. et al. Solving jigsaw puzzles by computer. Ann Oper Res 12, 51–64 (1988).

Download citation

  • Issue Date:

  • DOI: