Georgia Tech: Randomized Algorithms, Winter 1999 (CS 8113F)

Instructor: Leonard Schulman

CRN: 14513

Credit Hours: 3-0-3

Time: MW 3-4:30 CCB 101

Books: Motwani-Raghavan (Cambridge) and Alon-Spencer-Erdos (Wiley)

First Announcement

Second Announcement

Problem Set 1 (due date postponed to Feb 1)

Problem Set 2

Scribe notes: lecture 1, ``Min-Cut''

Scribe notes: lecture 2, ``\#SAT''

Scribe notes: lecture 3, ``Approximate $\#DNF$ (cont.) and the Chernoff Bound''

Scribe notes: lecture 4, ``Johnson-Lindenstrauss Embedding''

Scribe notes: lecture 5, ``Johnson-Lindenstrauss Embedding (cont.)''

Scribe notes: lecture 6, ``Fisher Information and the Cramer-Rao-Frechet Bound''

Scribe notes: lectures 7 & 8, ``$k$-wise independent sets, error correcting codes and metric space embeddings''

Scribe notes: lecture 9, ``Approximate Isometries from $4$-wise Independent Sample Spaces''

Scribe notes: lecture 10, ``Finding a maximal independent set is in NC''

lectures 11, 12, 13: ``Clustering''

Scribe notes: lectures 14 & 15, ``Expander graphs and pseudorandom number generators for BPP''

Scribe notes: lectures 16 & 17, ``Finding Perfect Matchings''

D. R. Karger. Global min-cuts in RNC, and other ramifications of a simple min-cut algorithm. Proc. 4'th ACM-SIAM SODA, 21-30, 1993.

D. R. Karger and C. Stein. An O~(n^2) algorithm for minimum cuts. Proc. 25'th ACM STOC, 757-765, 1993.

R. M. Karp, M. Luby and N. Madras. Monte-Carlo approximation algorithms for enumeration problems. J. Algorithms, 10:429-448, 1989.

W. B. Johnson and J. Lindenstrauss, Extensions of Lipschitz mappings into a Hilbert space, Contemp. Math. 26:189-206, 1984.

H. Cramer, A contribution to the theory of statistical estimation, Skandinavisk Aktuarietidskrift, 29:85-94, 1946

C. R. Rao, Information and accuracy attainable in estimation of statistical parameters, Bull. Cal. Math. Soc., 37:81-91, 1945.

M. Frechet, sur l'extension de certain evaluations statistique au cas des petit echantillons, Rev. Inst. Stat., 11:182-205, 1943.

N. Alon, L. Babai and A. Itai, A fast and simple randomized parallel algorithm for the maximal independent set problem, J. Algorithms 7:567-583, 1986

B. Chor, O. Goldreich, J. Hastad, J. Friedman, S. Rudich and R. Smolenski, The Bit Extraction Problem or t-Resilient Functions, Proc. 26'th FOCS, 396-407, 1985.

B. Berger, The fourth moment method, Proc. 2'nd ACM-SIAM SODA, 373-383, 1991.

M. Luby, A Simple Parallel Algorithm for the Maximal Independent Set Problem, SIAM J. Comput. 15(4): 1036-1053, 1986

L. J. Schulman, Clustering for edge-cost minimization, manuscript.

M. M. Deza and M. Laurent, Geometry of Cuts and Metrics, Springer 1997.

N. Linial, E. London and Y. Rabinovich, The geometry of graphs and some of its algorithmic applications, Proc. 35'th FOCS, 577-591, IEEE Press, 1994

R. Impagliazzo and D. Zuckerman, How to recycle random bits, 248-253, FOCS 1989

M. O. Rabin and V. V. Vazirani, Maximum matchings in general graphs through randomization. J. Algorithms 10(4):557-567, 1989.

K. Mulmuley, U. V. Vazirani and V. V. Vazirani, Matching is as easy as matrix inversion. Combinatorica 7:105-113, 1987.