Converting Online Algorithms to Local Computation Algorithms

  • Yishay Mansour
  • Aviad Rubinstein
  • Shai Vardi
  • Ning Xie
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)


We propose a general method for converting online algorithms to local computation algorithms, by selecting a random permutation of the input, and simulating running the online algorithm. We bound the number of steps of the algorithm using a query tree, which models the dependencies between queries. We improve previous analyses of query trees on graphs of bounded degree, and extend this improved analysis to the cases where the degrees are distributed binomially, and to a special case of bipartite graphs.

Using this method, we give a local computation algorithm for maximal matching in graphs of bounded degree, which runs in time and space O(log3 n).

We also show how to convert a large family of load balancing algorithms (related to balls and bins problems) to local computation algorithms. This gives several local load balancing algorithms which achieve the same approximation ratios as the online algorithms, but run in O(logn) time and space.

Finally, we modify existing local computation algorithms for hypergraph 2-coloring and k-CNF and use our improved analysis to obtain better time and space bounds, of O(log4 n), removing the dependency on the maximal degree of the graph from the exponent.


Bipartite Graph Random Permutation Online Algorithm Distribute Hash Table Minimum Vertex Cover 
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.


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  1. 1.
    Alon, N., Rubinfeld, R., Vardi, S., Xie, N.: Space-efficient local computation algorithms. In: Proc. 23rd ACM-SIAM Symposium on Discrete Algorithms, pp. 1132–1139 (2012)Google Scholar
  2. 2.
    Azar, Y., Broder, A.Z., Karlin, A.R., Upfal, E.: Balanced allocations. SIAM Journal on Computing 29(1), 180–200 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Beck, J.: An algorithmic approach to the Lovász Local Lemma. Random Structures and Algorithms 2, 343–365 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Berenbrink, P., Brinkmann, A., Friedetzky, T., Nagel, L.: Balls into non-uniform bins. In: Proceedings of the 24th IEEE International Parallel and Distributed Processing Symposium (IPDPS), pp. 1–10. IEEE (2010)Google Scholar
  5. 5.
    Berenbrink, P., Czumaj, A., Steger, A., Vöcking, B.: Balanced allocations: The heavily loaded case. SIAM J. Comput. 35(6), 1350–1385 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press (1998)Google Scholar
  7. 7.
    Byers, J.W., Considine, J., Mitzenmacher, M.: Simple Load Balancing for Distributed Hash Tables. In: Kaashoek, M.F., Stoica, I. (eds.) IPTPS 2003. LNCS, vol. 2735, pp. 80–88. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Dubhashi, D., Ranjan, D.: Balls and bins: A study in negative dependence. Random Structures and Algorithms 13, 99–124 (1996)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Marko, S., Ron, D.: Distance Approximation in Bounded-Degree and General Sparse Graphs. In: Díaz, J., Jansen, K., Rolim, J.D.P., Zwick, U. (eds.) APPROX 2006 and RANDOM 2006. LNCS, vol. 4110, pp. 475–486. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Mitzenmacher, M., Richa, A., Sitaraman, R.: The power of two random choices: A survey of techniques and results. In: Pardalos, P., Rajasekaran, S., Reif, J., Rolim, J. (eds.) Handbook of Randomized Computing, vol. I, pp. 255–312. Kluwer Academic Publishers, Norwell (2001)Google Scholar
  11. 11.
    Nguyen, H.N., Onak, K.: Constant-time approximation algorithms via local improvements. In: Proc. 49th Annual IEEE Symposium on Foundations of Computer Science, pp. 327–336 (2008)Google Scholar
  12. 12.
    Parnas, M., Ron, D.: Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms. Theoretical Computer Science 381(1–3) (2007)Google Scholar
  13. 13.
    Rubinfeld, R., Tamir, G., Vardi, S., Xie, N.: Fast local computation algorithms. In: Proc. 2nd Symposium on Innovations in Computer Science, pp. 223–238 (2011)Google Scholar
  14. 14.
    Talwar, K., Wieder, U.: Balanced allocations: the weighted case. In: Proc. 39th Annual ACM Symposium on the Theory of Computing, pp. 256–265 (2007)Google Scholar
  15. 15.
    Vöcking, B.: How asymmetry helps load balancing. J. ACM 50, 568–589 (2003)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Yoshida, Y., Yamamoto, Y., Ito, H.: An improved constant-time approximation algorithm for maximum matchings. In: Proc. 41st Annual ACM Symposium on the Theory of Computing, pp. 225–234 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yishay Mansour
    • 1
  • Aviad Rubinstein
    • 1
  • Shai Vardi
    • 1
  • Ning Xie
    • 2
  1. 1.School of Computer ScienceTel Aviv UniversityIsrael
  2. 2.CSAIL, MITCambridgeUSA

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