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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)

Abstract

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.

Keywords

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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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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