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Parallel Algorithms

  • Gerhard Winkler
Part of the Applications of Mathematics book series (SMAP, volume 27)

Abstract

In the previously considered relaxation algorithms, current configurations were updated sequentially: The Gibbs sampler (possibly) changed a given configuration x in a systematically or randomly chosen site s, replacing the old value x s by a sample y s from the local characteristic П(x s |xS\{s}) The next step started from the new configuration y = y s x S \{s}. More generally, on a (random) set AS the subconfiguration x A could be replaced by a sample from П(y A |x S \A) and the next step started from y = y A x S \A. The latter reduces the number of steps needed for a good estimate but in general does not result in a substantial gain of computing time. The computational load in each step increases as the subsets get larger; for large A (A = S) the algorithms even become computationally infeasible.

Keywords

Ising Model Parallel Algorithm Chromatic Number Pair Potential Transition Kernel 
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 1995

Authors and Affiliations

  • Gerhard Winkler
    • 1
  1. 1.Mathematical InstituteLudwig-Maximilians UniversitätMünchenGermany

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