Approximation algorithms for dynamic storage allocation

  • Jordan Gergov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1136)


We present a new O(n log n)-time 5-approximation algorithm for the NP-hard dynamic storage allocation problem (DSA). The two previous approximation algorithms for DSA are based on on-line coloring of interval graphs and have approximation ratios of 6 and 80 [6, 7, 16]. Our result gives an affirmative answer to the important open question of whether the approximation ratio of DSA can be improved below the bound implied by on-line coloring of interval graphs [7, 16]. Our approach is based on the novel concept of a 2-allocation and on the design of an efficient transformation of a 2-allocation to an at most 5/2 times larger memory allocation.

For the NP-hard variant of DSA with only two sizes of blocks allowed, we give a simpler 2-approximation algorithm. Further, by means of a tighter analysis of the widely used First Fit strategy, we show how the competitive ratio of on-line DSA can be improved to Θ(max{1, log(nk/M)}) where M, k, and n are upper bounds on the maximum number of simultaneously occupied cells, the maximum number of blocks simultaneously in the storage, and the maximum size of a block.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A.V. Aho, J.E. Hopcroft, and J.D. Ullman, Data structures and algorithms, Addison-Wesley, 1983.Google Scholar
  2. [2]
    M. Chrobak, M. Slusarek, On some packing problem related to dynamic storage allocation, RAIRO Informatique Theorique et Applications 22 (1988), pp. 487–499.Google Scholar
  3. [3]
    D. Detlefs, A. Dosser, and B. Zorn, Memory allocation costs in large C and C++ programs, Software: Practice and Experience, 24 (6), 1994, pp. 527–542.Google Scholar
  4. [4]
    M.R. Garey and D.S. Johnson, Computers and Intractability—A Guide to the Theory of NP-Completeness, Freeman, (1979).Google Scholar
  5. [5]
    H.A. Kierstead and W.T. Trotter, An extremal problem in recursive combinatorics, Congr. Numerantium 33 (1981), pp. 143–153.Google Scholar
  6. [6]
    H.A. Kierstead, The linearity of first-fit coloring of interval graphs, SIAM J. Disc. Math. 1 (1988), pp. 526–530.Google Scholar
  7. [7]
    H.A. Kierstead, A polynomial time approximation algorithm for Dynamic Storage Allocation, Discrete Mathematics 88 (1991), pp. 231–237.Google Scholar
  8. [8]
    K. Knowlton, A fast storage allocator, Comm. of ACM, Vol. 8, 1965, pp. 623–625.Google Scholar
  9. [9]
    D.E. Knuth, The Art of Computer Programming, Vol. 1: Fundamental algorithms, 2nd Edition, Addison-Wesley, Reading, MA, 1973.Google Scholar
  10. [10]
    S. Krogdahl, A dynamic storage allocation problem, Information Processing Letters, 2, 1973, pp. 96–99.Google Scholar
  11. [11]
    M.G. Luby, J. Naor, and A. Orda, Tight bounds for dynamic storage allocation, in Proc. 5th Annual ACM-SIAM Symp. on Discrete Algorithms, 1994, pp. 724–732.Google Scholar
  12. [12]
    J.M. Robson, An estimate of the store size necessary for dynamic storage allocation, J. ACM, Vol. 18, 1971, pp. 416–423.Google Scholar
  13. [13]
    J.M. Robson, Bounds for some functions concerning dynamic storage allocation, J. ACM, Vol. 12, 1974, pp. 491–499.Google Scholar
  14. [14]
    J.M. Robson, Worst case fragmentation of first fit and best fit storage allocation strategies, Computer Journal, Vol. 20, 1977, pp. 242–244.Google Scholar
  15. [15]
    M. Slusarek, NP-Completeness of Storage Allocation, Jagiellonian U. Scientific Papers, s. Informatics 3 (1987), pp. 7–18.Google Scholar
  16. [16]
    M. Slusarek, A coloring algorithm for interval graphs, in Proc. 14th Mathematical Foundations of Computer Science (1989), LNCS 379, Springer, pp. 471–480.Google Scholar
  17. [17]
    T.A. Standish, Data structures techniques, Addison-Wesley Publishing Company, 1980.Google Scholar
  18. [18]
    D.R. Woodall, Problem No. 4, in Proc. British Combinatorial Conference (1973), London Math. Soc. Lecture Notes Series 13, Cambridge University Press, 1974, p. 202Google Scholar
  19. [19]
    D.R. Woodall, The bay restaurant—a linear storage problem, American Mathematical Monthly, Vol. 81, 1974, pp. 240–246.Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Jordan Gergov
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

Personalised recommendations