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Pseudorandom Number Generators and Skip Lists: Efficient Data Structure Design

Explore pseudorandom number generators like Middle-square method, Mersenne Twister, Blum- Blum-Shub, and skip lists' advantages in algorithm design. Learn efficient data structuring techniques with skip lists implementation.

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Pseudorandom Number Generators and Skip Lists: Efficient Data Structure Design

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  1. Skip Lists Nov. 2, 2006

  2. Midterm #2 • Nov. 9 Thu 7pm

  3. Pseudorandom number generator • Middle-square method (John von Neumann, 1946) • Take any number, square it, remove the middle digits of the resulting number as your "random number", then use that number as the seed for the next iteration • 111101234321 2343 05489649 4896…

  4. Pseudorandom number generator • Mersenne twister (Makoto Matsumoto and Takuji Nishimura, 1997) • Has the colossal period of 219937-1 iterations • Its output is predictable

  5. Pseudorandom number generator • Cryptographically secure pseudorandom number generator • Blum-Blum-Shub • (Lenore Blum, Manuel Blum and Michael Shub, 1986)

  6. Skip Lists • The main advantage of using randomization in data structure and algorithm design is that the structures and functions that result are usually simple and efficient.

  7. Skip Lists • Page 396 Searching  • Page 398 Insertion  • Page 399 Removal 

  8. Skip Lists • We do not actually need to store pointers to items at the levels of the skip list above 0. • We do not actually need the above() method. In fact, we do not need the before() function either.

  9. Maintaining the Top-most Level • Top-level capping • h = max {10, 2 } • h = 3 • Top-level freedom

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