The traveling cameraman problem, with applications to automatic optical inspection

Extended abstract
  • Kazuo Iwano
  • Prabhakar Raghavan
  • Hisao Tamaki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 834)


We are given a finite set of disjoint regions in the plane. We wish to cover all the regions by unit squares, and compute a path that visits the centers of all the unit squares in the cover. Our objective is to minimize the length of this path. The problem arises in the automatic optical inspection of printed circuit boards and other assemblies.

We show that a natural heuristic yields a path of length at most a constant times optimal, whenever the problem of covering the regions by the minimum number of unit squares can be approximated to within a constant. We consider a generalization in which the regions may be covered by squares of different sizes, and for each input region we are given an upper bound on the size of the permissible square. We show that a simple extension of our heuristic is provably good in this case as well.


Print Circuit Board Travel Salesman Problem Covering Problem Optimal Covering Disjoint Region 
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  1. 1.
    E. Arkin and R. Hassin. Approximation algorithms for the geometric covering salesman problem. Technical Report 968, School of Operations Research and Industrial Engineering, Cornell University, 1991. To appear: Discrete Applied Math.Google Scholar
  2. 2.
    E. Arkin, S. Fekete, J. Mitchell and C. Piatko. Optimal Covering Tour Problems. Manuscript 1993.Google Scholar
  3. 3.
    N. Christofides. Worst-case Analysis of a New Heuristic for the Traveling Salesman Problem. Technical Report, GSIA, Carnegie-Mellon Univ., 1976.Google Scholar
  4. 4.
    J. Current and D. Schilling. The Covering Salesman Problem. Transportation Science 23, 208–213, 1989.Google Scholar
  5. 5.
    P. Forte et al. Automatic Inspection of Electronic Surface Mount Assemblies. Proceedings of SPIE — International Society of Optical Engineering, Intelligent Robots and Computer Vision XII: Algorithms and Techniques, vol. 2055, 50–56, 1993.Google Scholar
  6. 6.
    S. Hata. Vision Systems for PCB Manufacturing in Japan. IECON '90, 16th Annual Conference of IEEE Industrial Electronics Society, vol. 1, 792–797, 1990.Google Scholar
  7. 7.
    M.E. Hernandes, J.R. Villalobos, and W.C. Johnson. Sequential Computer Algorithms for Printed Circuit Board Inspection. Proceedings of SPIE — International Society of Optical Engineering, Intelligent Robots and Computer Vision XII: Active Vision and 3D Methods, vol. 2056, 438–449, 1993.Google Scholar
  8. 8.
    D.S. Hochbaum and W. Maass. Approximation Schemes for Covering and Packing Problems in Image Processing and VLSI. Journal of the ACM, 32:130–136, January 1985.Google Scholar
  9. 9.
    K. Iwano, P. Raghavan and H. Tamaki. The Traveling Cameraman Problem, with Applications to Automatic Optical Inspection. IBM Technical Report, 1994Google Scholar
  10. 10.
    L. Lovász. On the ratio of optimal integral and fractional covers. Discrete Math., 13:383–390, 1975.CrossRefGoogle Scholar
  11. 11.
    S.H. Oguz and L. Onural. An Automated System for Design Rule Based Visual Inspection of Printed Circuit Boards. Proceedings of the 1991 IEEE International Conference on Robotics and Applications, vol. 3, 2696–2701, 1991.Google Scholar
  12. 12.
    C.H. Papadimitriou. The Euclidean Traveling Salesman Problem is NP-Complete. Theoretical Computer Science, 4:237–244, 1977.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Kazuo Iwano
    • 1
  • Prabhakar Raghavan
    • 2
  • Hisao Tamaki
    • 2
  1. 1.IBM Tokyo Research LaboratoryKanagawaJapan
  2. 2.IBM T.J. Watson Research CenterYorktownUSA

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