Models and Problems of Dynamic Memory Allocation

  • V. E. Beneš
Part of the Progress in Computer Science book series (PCS, volume 2)

Abstract

We construct and analyze some stochastic models for optimal allocation of memory in fragmented arenas. The arenas, as well as the item types they carry, are of various shapes: linear, cubic, pentagonal pie, S2 (surface of sphere). Formulated as a Markov dynamic programming problem, the choice of optimal memory allocation closely resembles the choice of an optimal route for a telephone call. Much can be guessed about optimal operation from scrutiny of the partial ordering of the possible states reduced under symmetries; especially, in many specific examples, a natural relation B (read “better than ”) of preference can be defined among alternative allocations, and a topological fixed-point argument based on B given, to solve the allocation problem without resort to numerical solution of the Bellman equation.

Keywords

Hexagonal Arena Folk Alloca 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    E. G. Coffman, Jr., Kimming So, M. Hofri, and A. C. Yao, “A Stochastic Model of Binpacking,” Inf. and Control, 44 (1980), pp. 105–115, last paragraph.CrossRefGoogle Scholar
  2. [2]
  3. [3]
    D. E. Knuth, The Art of Computer Programming: Fundamental Algorithms (Vol. 1, 2nd Ed.), Addison-Wesley, Reading, Mass., 1973, p. 435 ff.Google Scholar
  4. [4]
    V. E. Benes, “Reduction of Network States Under Symmetries,” Bell System Tech. J., 57, (1978), pp. 111–149.Google Scholar
  5. [5]
    V. E. Benes, “Programming and Control Problems Arising from Optimal Routing in Telephone Networks,” Bell Systems Tech. J. 49, (1966), pp. 1373–1438.Google Scholar
  6. [6]
    N. Dunford and J. T. Schwartz, Linear Operators: General Theory (Part I), Interscience, New York, 1958, p. 456.Google Scholar
  7. [7]
    R. Bellman, Introduction to Matrix Analysis, McGraw-Hill, 1960, p. 294, exercise 8.Google Scholar

Copyright information

© Birkhäuser Boston, Inc. 1982

Authors and Affiliations

  • V. E. Beneš
    • 1
  1. 1.Bell LaboratoriesMurray HillUSA

Personalised recommendations