PRAM Models and Fundamental Parallel Algorithmic Techniques: Part II (Randomized Algorithms) (1998)
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BibTeX
@MISC{Spirakis98prammodels,
author = {Paul G. Spirakis},
title = {PRAM Models and Fundamental Parallel Algorithmic Techniques: Part II (Randomized Algorithms)},
year = {1998}
}
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Abstract
There are many fields of algorithms design where probabilistic methods and randomization lead to appreciable gains. In fact, randomness has emerged as a fundamental tool in the design and analysis of algorithms. It is substantially easier to obtain algorithms for many problems if we allow the use of randomness as a resource. This has been demonstrated for parallel algorithms as well. In this chapter, we highlight some fundamental randomization techniques and also discuss the class RNC of problems efficiently solved by probabilistic parallel algorithms. 1. Randomized Parallel Algorithms and the class RNC What does efficiency mean for a parallel algorithm? Roughly, we mean that it runs fast and uses not-too-many processors. This has been crystallized in the theoretical community in the notion of the complexity class NC, i.e. the class 1 of algorithms running in polylogarithmic (in the length of the input) time with polynomially many processors. Similarly, RNC (Randomized NC) is the cl...
