description Sanjeev Arora Overview
Sanjeev Arora is an American theoretical computer scientist and a professor at Princeton University. He is best known for his co-discovery of the PCP theorem in 1998, a landmark result in computational complexity theory that established the hardness of approximating many NP-hard problems. His research focuses on algorithms, complexity theory, and the geometric foundations of machine learning. He has received multiple accolades, including the Gödel Prize for his work on the PCP theorem.
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Sanjeev Arora ranks #22 of 185 in the Computer Scientist ranking, behind Tony Hoare, ahead of Niklaus Wirth.
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What is the PCP theorem and what was Sanjeev Arora's role in proving it?
The PCP theorem states that mathematical proofs can be rewritten so a verifier only needs to check a constant number of randomly chosen bits to be convinced of correctness with high probability. Arora, along with Carsten Lund, Rajeev Motwani, Madhu Sudan, and Mario Szegedy, proved the theorem in 1992, revolutionizing the understanding of proof verification and approximation hardness.
What is the connection between the PCP theorem and hardness of approximation?
Arora's PCP theorem work implied that many NP-hard optimization problems cannot be efficiently approximated within certain ratios unless P = NP. For example, it showed that there is no polynomial-time approximation scheme for MAX-3SAT, resolving long-standing questions about how well NP-hard problems can be approximated.
What is Arora's 'Computational Complexity: A Modern Approach' textbook?
Co-authored with Boaz Barak, this graduate-level textbook covers modern complexity theory including PCP, circuit lower bounds, quantum complexity, and proof complexity. It is widely used in graduate courses and is known for incorporating developments from the 1990s and 2000s that earlier textbooks did not cover.
Where does Sanjeev Arora work and what awards has he received?
Arora is the Charles C. Fitzmorris Professor of Computer Science at Princeton University, where he has been on the faculty since 1994. He received his PhD from UC Berkeley under Umesh Vazirani and has twice won the Gödel Prize — in 2001 for the PCP theorem and again in 2010 for his work on graph partitioning with Satish Rao and Umesh Vazirani.
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