Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Memory-Constrained Algorithms

  • Matias KormanEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_586-1

Years and Authors of Summarized Original Work

  • 1980; Munro, Patterson

  • 2000; Reingold

  • 2013; Barba, Korman, Langerman, Sadakane, Silveira

Problem Definition

This field of research evolves around the design of algorithms in the presence of memory constraints. Research on this topic has been going on for over 40 years [16]. Initially, this was motivated by the high cost of memory space. Afterward, the topic received a renewed interest with appearance of smartphones and other types of handheld devices for which large amounts of memory are either expensive or not desirable.

Although many variations of this principle exist, the general idea is the same: the input is in some kind of read-only data structure, the output must be given in a write-only structure, and in addition to these two structures, we can only use a fixed amount of memory to compute the solution. This memory should be enough to cover all space requirements of the algorithm (including the variables directly used by the...

Keywords

Connectivity Constant workspace Logspace Multi-pass algorithms One-pass algorithms Selection Sorting Stack algorithms Streaming Time-space trade-off Undirected graphs 
This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Aleliunas R, Karp RM, Lipton R, Lovasz L, Rackoff C (1979) Random walks, universal traversal sequences, and the complexity of maze problems. In: FOCS, San Juan, pp 218–223Google Scholar
  2. 2.
    Armoni R, Ta-Shma A, Widgerson A, Zhou S (2000) An o(log(n)4∕3) space algorithm for (s, t) connectivity in undirected graphs. J ACM 47(2):294–311MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Asano T, Rote G (2009) Constant-working-space algorithms for geometric problems. In: CCCG, Vancouver, pp 87–90Google Scholar
  4. 4.
    Asano T, Buchin K, Buchin M, Korman M, Mulzer W, Rote G, Schulz A (2012) Memory-constrained algorithms for simple polygons. Comput Geom Theory Appl 46(8):959–969MathSciNetCrossRefGoogle Scholar
  5. 5.
    Barba L, Korman M, Langerman S, Silveira R (2014) Computing the visibility polygon using few variables. Comput Geom Theory Appl 47(9):918–926MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Barba L, Korman M, Langerman S, Sadakane K, Silveira R (2015) Space-time trade-offs for stack-based algorithms. Algorithmica 72(4):1097–1129MathSciNetCrossRefGoogle Scholar
  7. 7.
    Blum M, Floyd RW, Pratt VR, Rivest RL, Tarjan RE (1973) Time bounds for selection. J Comput Syst Sci 7(4):448–461MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Borodin A, Cook S (1982) A time-space tradeoff for sorting on a general sequential model of computation. SIAM J Comput 11:287–297MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Chan TM (2010) Comparison-based time-space lower bounds for selection. ACM Trans Algorithms 6:1–16MathSciNetGoogle Scholar
  10. 10.
    Elmasry A, Juhl DD, Katajainen J, Satti SR (2013) Selection from read-only memory with limited workspace. In: COCOON, Hangzhou, pp 147–157Google Scholar
  11. 11.
    Frederickson GN (1987) Upper bounds for time-space trade-offs in sorting and selection. J Comput Syst Sci 34(1):19–26MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Jarvis R (1973) On the identification of the convex hull of a finite set of points in the plane. Inf Process Lett 2(1):18–21MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Munro JI, Paterson M (1980) Selection and sorting with limited storage. Theor Comput Sci 12:315–323MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Nisan N, Szemeredi E, Wigderson A (1992) Undirected connectivity in o(l o g 1. 5 n) space. In: FOCS, Pittsburg, pp 24–29Google Scholar
  15. 15.
    Pagter J, Rauhe T (1998) Optimal time-space trade-offs for sorting. In: FOCS, Palo Alto, pp 264–268Google Scholar
  16. 16.
    Pohl I (1969) A minimum storage algorithm for computing the median. IBM technical report RC2701Google Scholar
  17. 17.
    Raman V, Ramnath S (1998) Improved upper bounds for time-space tradeoffs for selection with limited storage. In: SWAT ’98, Stockholm, pp 131–142Google Scholar
  18. 18.
    Reingold O (2008) Undirected connectivity in log-space. J ACM 55(4):1–24MathSciNetCrossRefGoogle Scholar
  19. 19.
    Savitch WJ (1970) Relationships between nondeterministic and deterministic tape complexities. J Comput Syst Sci 4(2):177–192MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Graduate School of Information SciencesTohoku UniversityMiyagiJapan