Course Description

Which papers have had the most significant impact on the Theory of Computing, and in particular on shaping the modern Algorithmic Thinking? Not an easy question to answer as everyone has their own favorites. This course will focus on some of my own favorites. I have chosen these papers for their intrinsic beauty, as well as their long lasting influence on the field. Many of these papers have led to Turing Awards and Nevanlinna Prizes for their authors (e.g. Karp, Tarjan, Rivest-Shamir-Adleman, Valiant), as well foreshadowed entire new subfields within computer science (online algorithms, competitive analysis, computational learning theory, computational geometry, public key cryptography).

A tentative List of possible papers for students to present.

The Selection and Sorting with Limited Storage paper.

A Sampler of Classics

• A Planar Separator Theorem and its Applications, by Lipton and Tarjan (Nevanlinna Prize '82 and Turing award '86). A fundamental result on planar graphs, with many applications.

• A Theory of the Learnable, by Leslie Valiant (Nevanlinna Prize in '86). This paper started the field of Computational Learning Theory, formalizing concept learning by examples.

• Amortized Efficient of List Update and Paging Rules, by Sleator and Tarjan. This paper formalized the modern algorithm analysis concepts of amortized analysis and competitive ratios.

• Competitive Paging Algorithms, by Karp (Turing award '85) et al. Extends Sleator-Tarjan models and derives bounds for fundamental problems including caching and k servers.

• A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, by Rivest, Shamir, and Adleman (Turing award '02). The famous RSA algorithm.

• Making Data Structures Persistent, by Driscoll, Sarnak, Tarjan, and Sleator. This classic paper gives a general technique for making any standard (ephemeral) data structure into a persistent data structure.

• Bounds for Certain Multiprocessor Anomalies, by Ron Graham. This 1966 (!) paper foreshadows Online Algorithms and Competitive analysis by 25 years.

• Selection and Sorting with Limited Storage, by Munro and Paterson. This 1980 paper was analyzing streaming algorithms in 1980 before there was streaming, and giving surprising lower bounds.

• Geometric Complexity, by Shamos, and Multidimensional Divide and Conquer, by Jon Bentley, founded the field of Computational Geometry, giving powerful conceptual tools and data structures for multi-dimensional data.

This is a preliminary list, and a few more gems will be added for the complete course.

A tentative Schedule for the lectures.

The course style will be a mix of lectures by the professor, open discussion, and presentations by students. Because these topics span a broad spectrum of research in computer science foundations, students must be well-versed in algorithm analysis and comfortable with conceptual arguments and mathematical proofs, especially reasoning based on combinatorial and graph theoretic concepts. In addition, they should be able to extract the underlying core ideas of theory research papers and explain them in class presentations.