Papadimitriou Complexity Theory

[Trinidad Baltzell]

Papadimitrioustudied at the National Technical University of Athens, where in 1972 he received his Bachelor of Arts degree in electrical engineering. He then pursued graduate studies at Princeton University, where he received his Ph.D. in electrical engineering and computer science in 1976 after completing a doctoral dissertation titled "The complexity of combinatorial optimization problems."[9]

Papadimitriou has taught at Harvard, MIT, the National Technical University of Athens, Stanford, UCSD, University of California, Berkeley and is currently the Donovan Family Professor of Computer Science at Columbia University.

Papadimitriou co-authored a paper on pancake sorting with Bill Gates, then a Harvard undergraduate. Papadimitriou recalled "Two years later, I called to tell him our paper had been accepted to a fine math journal. He sounded eminently disinterested. He had moved to Albuquerque, New Mexico to run a small company writing code for microprocessors, of all things. I remember thinking: 'Such a brilliant kid. What a waste.'" The company was Microsoft.[10]

Papadimitriou co-authored "The Complexity of Computing a Nash Equilibrium" with his students Constantinos Daskalakis and Paul W. Goldberg, for which they received the 2008 Kalai Game Theory and Computer Science Prize from the Game Theory Society for "the best paper at the interface of game theory and computer science",[11] in particular "for its key conceptual and technical contributions";[12] and the Outstanding Paper Prize from the Society for Industrial and Applied Mathematics.

In 2001, Papadimitriou was inducted as a Fellow of the Association for Computing Machinery and in 2002 he was awarded the Knuth Prize. Also in 2002, he became a member of the U.S. National Academy of Engineering for contributions to complexity theory, database theory, and combinatorial optimization.[13] In 2009 he was elected to the US National Academy of Sciences. During the 36th International Colloquium on Automata, Languages and Programming (ICALP 2009), there was a special event honoring Papadimitriou's contributions to computer science.[14] In 2012, he, along with Elias Koutsoupias, was awarded the Gdel Prize for their joint work on the concept of the price of anarchy.[15]

Papadimitriou is the author of the textbook Computational Complexity, one of the most widely used textbooks in the field of computational complexity theory. He has also co-authored the textbook Algorithms (2008) with Sanjoy Dasgupta and Umesh Vazirani, and the graphic novel Logicomix (2009)[16] with Apostolos Doxiadis.

Papadimitriou was awarded the IEEE John von Neumann Medal in 2016, the EATCS Award in 2015, the Gdel Prize in 2012, the IEEE Computer Society Charles Babbage Award in 2004, and the Knuth Prize in 2002. In 2019 he received the Harvey Prize of the Technion/Israel for the year 2018.[19]

We research the fundamental capabilities and limitations of efficient computation. In addition, we use computation as a lens to gain deeper insights into problems from the natural, social, and engineering sciences. Our active research areas include algorithmic game theory, complexity theory, cryptography, the design and analysis of algorithms, interactive computation and communication, theoretical neuroscience, property testing, the role of randomness in computation, sublinear and streaming algorithms, and the theoretical foundations of machine learning.

Our group is highly collaborative, both within Columbia and among peer institutions. We have a weekly Theory Lunch and Student Seminar. We also have an Undergraduate Theory Learning Seminar that organizes student-run reading groups for undergraduates. Most graduate students have (at least) two advisors and collaborate with several professors and other students. Some of our faculty are cross-listed with the IEOR department and the Data Science Institute. We interact with the New York theory community at large through NYCAC, NYC Theory Day, NYC Crypto Day, and the Simons Collaboration on Algorithms and Geometry.

We regularly communicate on two listservs, which you can join on the attached links: theory-read (for seminar talks that include faculty) and theory-phd (for student-centric things, including our student seminar).

Our department and research group are growing, and we're always looking for new members and collaborators. If you would like to join our group as a graduate student, please apply to the PhD program in Computer Science at Columbia. Please reach out to faculty directly for inquiries about postdoc positions.

Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors).

Computational Complxity is not a formal class at ETSU. These notes are meant for self-study and reference.Classes which cover similar topics are offered by the Department of Computer Science (these class descriptions are from the ETSU 2022-23 Graduate Catalog): Formal Languages and Computational Complexity (CSCI 5610). Prerequisites: MATH 2710, CSCI 2210 or consent of the instructor.Problem-solving is a fundamental aspect of computer science. This course teaches students how to reduce a computational problem to its simplest form and analyze the problem to determine its inherent computational complexity. Topics include formal languages and automata theory, Turing machines, computational complexity, and the theory of NP-completeness.When Offered: Variable. Analysis Of Algorithms (CSCI 5620).Prerequisites: Differential and integral calculus, discrete structures, data structures. This course covers basic techniques for analyzing algorithmic complexity. It describes the design and analysis of selected algorithms for solving important problems that arise often in applications of computer science, including sorting, selection, graph theory problems (e.g., shortest path, graph traversals), string matching, dynamic programming problems, NP-complete problems. When Offered: Fall, alternate years [odd falls].The first of these CSCI classes is most similar to the material presented here. However, Formal Languages and Computational Complexity (CSCI 5610) only has prerequisites of Discrete Structures (MATH 2710) or Data Structures (CSCI 2210). Discrete Structures (MATH 2710) was discontinued in the ealy 2000s, though I have online notes for Discrete Structures from the last time I taught it (spring 2001). For the notes presented here, prerequisite material would include Mathematical Reasoning (MATH 3000) and Introduction to Set Theory (not a formal ETSU class; some of this material is covered in Mathematical Reasoning, but not deeply). Some exposure to graph theory is desirable, since several of the initial problems encountered here involve graph theory problems. A sufficient background is given by Introduction to Graph Theory (MATH 4347/5347).

The combined work of Papadimitriou and Yannakakis, both from Columbia University, has focused on computational complexity theory and providing an understanding of the limits of efficient solvability for a wide range of decision and optimization problems central to operations research and the management sciences.

As an example of a major contribution, Papadimitriou and Yannakakis (1988) introduced Max-NP and Max-SNP, natural variants of the NP complexity class, comprising certain optimization problems that can be approximated with bounded error. Within these classes, they showed that several common problems have polynomial-time approximation schemes only if the whole class does.

The John von Neumann Theory Prize, one of INFORMS most prestigious prizes, is awarded at the 2023 INFORMS Annual Meeting in October in Phoenix, Arizona. The Prize typically reflects contributions that have stood the test of time. The criteria for the Prize are broad, and include significance, innovation, depth and scientific excellence.

As the largest professional association for the data and decision sciences, INFORMS members leverage mathematics and scientific methodologies to help organizations and governments at all levels make better, data-driven decisions. With more than 12,000 professional and student members from around the world, INFORMS members support organizations and governments at all levels as they work to transform data into information, and information into insights that save lives, save money and solve problems.

As the largest professional association for the data and decision sciences, INFORMS members leverage mathematics and scientific methodologies to help organizations and governments at all levels make better, data-driven decisions. With more than 12,000 professional and student members from around the world, INFORMS is the largest association for the decision and data sciences. INFORMS members support organizations and governments at all levels as they work to transform data into information, and information into insights that save lives, save money, and solve problems.

Vassiliki Voula Papadimitriou is a renowned computer scientist who has made significant contributions to the fields of theoretical computer science, algorithms, and complexity theory. She is a Professor of Computer Science at the University of California, Berkeley, and has received numerous awards for her work, including the MacArthur Fellowship and the Knuth Prize.

Papadimitriou's research has focused on the development of efficient algorithms for solving complex problems. She has made important contributions to the areas of approximation algorithms, online algorithms, and randomized algorithms. Her work has had a major impact on the design and analysis of algorithms for a wide range of applications, including scheduling, routing, and network optimization.

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