Approximation schemes for covering and packing problems in robotics and vlsi

Extended abstract
  • Dorit S. Hochbaum
  • Wolfgang Maass
Contibuted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 166)


The approach described in this paper, the shifting strategy, has proved useful in a large variety of contexts. Via the use of this approach we were able to derive algorithms that are the best possible in the sense that the exponential dependence on 1/ɛ cannot be removed unless NP=P. We also note that all other polynomial approximation schemes that we are familiar with rely on dynamic programming. The technique we introduced is an alternative to dynamic programming for the construction of polynomial approximation schemes for strongly NP-complete problems.


Approximation Algorithm Approximation Scheme Local Algorithm Packing Problem Performance Ratio 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    John J. Bartholdi III, "A Guaranteed-Accuracy Round-Off Algorithm for Cyclic Scheduling and Set Covering," Operations Research, Vol. 29, No. 3 (1981).Google Scholar
  2. [2]
    F. D. Berman, F. T. Leighton and L. Snyder, "Optimal Tile Salvage," unpublished manuscript (1982).Google Scholar
  3. [3]
    R. J. Fowler, M. S. Paterson, and S. L. Tanimoto, "Optimal Packing and Covering in the Plane Are NP-Complete," Inform. Process. Lett., 12 (1981), 133–137.Google Scholar
  4. [4]
    M. R. Gary and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman (1978).Google Scholar
  5. [5]
    D. S. Hochbaum and W. Maass, "Fast Approximation Algorithms for the Robot Placement Problem," manuscript, U.C. Berkeley (1983), submitted.Google Scholar
  6. [6]
    D. S. Hochbaum and W. Maass, "Approximation Algorithms for Covering and Packing Problems in Image Processing and VLSI," manuscript, U.C. Berkeley (May 1983), submitted.Google Scholar
  7. [7]
    D. S. Johnson, "The NP-Completeness Column: An Ongoing Guide," Journal of Algorithms, 3, 182–195 (1982).Google Scholar
  8. [8]
    W. Maass, "On the Complexity of Computing Optimal Positions for Industrial Robots," U.C. Berkeley, manuscript, submitted.Google Scholar
  9. [9]
    S. L. Tanimoto and R. J. Fowler, "Covering Image Subsets with Patches," Proc. 5th Inter. Conf. on Pattern Recognition, (1980) 835–839.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Dorit S. Hochbaum
    • 1
  • Wolfgang Maass
    • 2
  1. 1.University of California, BerkeleyBerkeley
  2. 2.Department of Computer ScienceUniversity of California, BerkeleyBerkeley

Personalised recommendations