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					Randomized “Algorithms”
Monte Carlo and Las Vegas Technuques
Randomized
   Monte Carlo
    ◦ Might give an incorrect answer (approximate) but always give
      an answer


   Las Vegas
    ◦ Might never give an answer (quit or run forever)


   Each uses some randomized technique to attack a
    problem
Monte Carlo Integration
float area(function f, float a, float b,
  float fMax, int n) {
  float x, y; int hits=0, trial;
  for (trial=0; trial<n; trial++) {
      x = a+random(b-a); y = random(fMax);
      if (f(x)>=y) hits++;
  }
  return((b-a)*fMax*hits/n);
}
Las Vegas and Ethernet
bool success = false;
while (!success) {
  status = message.send();
  success = status == TRANSMITTED;
  if (!success) wait a bit;
}
Las Vegas Dining Philosophers

   Discussed in class


Monte Carlo Illumination

    Discussed in class
References
   Some material from the textbook:
    Data Structures and Algorithm Analysis in Java (Second
     Edition) by Mark Allen Weiss
   Additional images:
    www.wikipedia.com

				
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posted:2/2/2013
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