MATHEMATICAL TECHNIQUES IN THE ANALYSIS OF ALGORITHMS

COMPSCI 787

Advanced paradigms for the design and analysis of efficient algorithms, including the use of randomness, linear programming, and semi-definite programming. Applications to data structures, approximating NP-hard optimization problems, learning, on-line and distributed problems. Students are strongly encouraged to have introductory knowledge of algorithms (e.g.,COMP SCI 577)

COMPSCI 812

Survey of algorithms and design paradigms for exact arithmetic, as used in public-key cryptography, computer algebra, and pseudo-random number generation. Topics include primality testing, factorization of integers and polynomials, discrete logarithms, and (optionally) elliptic curves and integer lattices. Students are strongly encourage to have knowledge of basic abstract algebra (e.g.,MATH 541), and intermediate programming ability (e.g., COMP SCI 367 orCOMP SCI 300).

COMPSCI 710

Study of the capabilities and limitations of efficient computation. Relationships between models representing capabilities such as parallelism, randomness, quantum effects, and non-uniformity; and models based on the notions of nondeterminism, alternation, and counting, which capture the complexity of important problems. Knowledge of the theory of computation is strongly encouraged, such asCOMP SCI 520.

COMPSCI 577

Basic paradigms for the design and analysis of efficient algorithms: greed, divide-and-conquer, dynamic programming, reductions, and the use of randomness. Computational intractability including typical NP-complete problems and ways to deal with them.

COMPSCI 880

Advanced topics in algorithms, complexity, and cryptography. The exact topic varies.