An approximation method for solving the sofa problem

  • Kiyoshi Maruyama


A procedure for the solution of the two-dimensional sofa problem is described. A new class of polygons, angularly simple polygons, is defined as a class of permissible sofas. The pattern representationSr(xo) developed for this class of polygons has the advantage of allowing easy polygonal transformations. The procedure called GSPS, described here, gives a good approximate solution to the sofa problem in reasonable time. Slight modification of the procedure leads to an algorithm for the solution of the general sofa problem.


Operating System Approximation Method Approximate Solution Slight Modification Reasonable Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    F. Attneave and M. D. Arnoult, “The quantitative study of shape and pattern perception,”Psycholog. Bull. 53(6):452–471 (1956).Google Scholar
  2. 2.
    J. E. Doran and D. Michie, “Experiments with graph traverser programs,”Proc. Roy. Soc. (A) 294 (September):235–259 (1966).Google Scholar
  3. 3.
    H. Freeman, “On the encoding of arbitrary geometric configurations,”IRE Trans. Electronic Computers EC-10 (June):260–268 (1961).Google Scholar
  4. 4.
    H. Freeman and L. Garder, “A pictorial jigsaw puzzle: The computer solution of a problem in pattern recognition,”IEEE Trans. Electronic Computers EC-13 (April): 118–127 (1964).Google Scholar
  5. 5.
    M. Goldberg, “A solution of problem 66-11: Moving furniture through a hallway,”SIAM Rev. 11(1):118–127 (1969).Google Scholar
  6. 6.
    W. E. Howden, “The sofa problem,”Computer J. 11(3):299–301 (1968).Google Scholar
  7. 7.
    A. Kaufmann,Graphs, Dynamic Programming and Finite Games (Academic Press, New York, 1967).Google Scholar
  8. 8.
    K. Maruyama, “A procedure for detecting intersections and its application,” Department of Computer Science, University of Illinois, Urbana, Illinois Report No. 449, May 1971.Google Scholar
  9. 9.
    K. Maruyama, unpublished paper, May 1971.Google Scholar
  10. 10.
    D. Michie, “Strategy-building with graph traversers,” N. L. Collins and D. Michie, eds., inMachine Intelligence, Vol. 1:3–15 (1967).Google Scholar
  11. 11.
    L. Moser, “Problem 66-11: Moving furniture through a hallway,”SIAM Rev. 8(3):381 (1966).Google Scholar
  12. 12.
    A. Newell and G. Ernst, “The search for generality,” inProc. IFIP Congress (1965), pp. 17–22.Google Scholar
  13. 13.
    I. Pohl, “Bidirectional and heuristic search in path problems,” SLAC Report, No. 104, May 1969.Google Scholar
  14. 14.
    I. Scoins, “Linear graphs and trees,” N. L. Collins and D. Michie, eds., in (Machine Intelligence, Vol. 1 (1967), pp. 3–15.Google Scholar
  15. 15.
    J. Sebastian, “A Solution of problem 66-11: Moving furniture through a hallway,”SIAM Rev. 12:582–586 (1970).Google Scholar
  16. 16.
    I. E. Sutherland, “A method for solving arbitrary wall mazes by computer,”IEEE Trans. Computers C-18(12):1092–1097 (1969).Google Scholar

Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • Kiyoshi Maruyama
    • 1
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbana

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