# random - IntroductiontoRandomizedAlgorithmsandthe...

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Lecture 20: April 12 Introduction to Randomized Algorithms and the  Introduction to Randomized Algorithms and the  Probabilistic Method Probabilistic Method

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Making Decision Flip a coin.
Making Decision Flip a coin! An algorithm which flip coins is called a  randomized algorithm.

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Why Ra ndo m ne s s ? A rando m ize d alg o rithm  is   simpler . Ma king  de c is io ns  c o uld be  c o m plic ate d. C o ns ide r the  m inim um  c ut pro ble m C a n be  s o lve d b y m a x flo w. Ra ndo m ize d a lg o rithm ? Pic k a ra ndo m  e dg e  a nd c o ntrac t. And re pe at until two  ve rtic e s  le ft.
Why Ra ndo m ne s s ? A rando m ize d a lg o rithm  is   faster . Ma king  g o o d de c is io ns  c o uld be  e xpe ns ive . C o ns ide r a  s o rting  pro c e dure . 5   9   13   8   11   6   7   10 5   6   7 8 9   13   11   10 Pic king  an e le m e nt in the  m iddle  m a ke s  the  pro c e dure  ve ry e ffic ie nt, b ut it is  e xpe ns ive  (i.e . line ar tim e ) to  find s uc h a n e le m e nt. Pic king  a rando m  e le m e nt will do .

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Why Ra ndo m ne s s ? A rando m ize d a lg o rithm  is   faster . Ma king  g o o d de c is io ns  c o uld be  e xpe ns ive .  Minim um  s pa nning  tre e s   A line a r tim e  ra ndo m ize d a lg o rithm , b ut no  kno wn line ar tim e  de te rm inis tic  a lg o rithm .  Prim a lity te s ting A rando m ize d po lyno m ial tim e  a lg o rithm , b ut it ta ke s  thirty ye ars  to  find a  de te rm inis tic  o ne .  Vo lum e  e s tim a tio n o f a  c o nve x b o dy A rando m ize d po lyno m ial tim e   approximation  a lg o rithm , b ut no  kno wn de te rm inis tic  po lyno m ial tim e  a ppro xim a tio n alg o rithm .
Why Ra ndo m ne s s ? Probabilistic method

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## This note was uploaded on 12/02/2011 for the course AR 107 taught by Professor Gracegraham during the Fall '11 term at Montgomery College.

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random - IntroductiontoRandomizedAlgorithmsandthe...

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