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- Sanjeev Arora, Boaz Barak
- 2009

Not to be reproduced or distributed without the authors' permission This is an Internet draft. Some chapters are more finished than others. References and attributions are very preliminary and we apologize in advance for any omissions (but hope you will nevertheless point them out to us).

- Sanjeev Arora, Shmuel Safra
- J. ACM
- 1992

We give a new characterization of NP: the class NP contains exactly those languages <italic>L</italic> for which membership proofs (a proof that an input <italic>x</italic> is in <italic>L</italic>) can be verified probabilistically in polynomial time using <italic>logarithmic</italic> number of random bits and by reading <italic>sublogarithmic</italic>â€¦ (More)

- Sanjeev Arora
- J. ACM
- 1998

We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed <italic>c</italic> > 1 and given any <italic>n</italic> nodes in <inline-equation><f><sc>R</sc></f> </inline-equation><supscrpt>2</supscrpt>, a randomized version of the scheme finds a (1 + 1/<italic>c</italic>)-approximation to the optimum travelingâ€¦ (More)

- Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, Mario Szegedy
- Electronic Colloquium on Computational Complexity
- 1998

We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a <italic>constant</italic> number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probability 1 (i.e., for every choice of its randomâ€¦ (More)

- Sanjeev Arora
- FOCS
- 1996

We present a polynomial time approximation scheme for Euclidean TSP in <2. Given any n nodes in the plane and > 0, the scheme finds a (1 + )-approximation to the optimum traveling salesman tour in time nO(1= ). When the nodes are in <d, the running time increases to nÃ•(logd 2 n)= d 1 . The previous best approximation algorithm for the problem (due toâ€¦ (More)

- Sanjeev Arora, Satish Rao, Umesh V. Vazirani
- STOC
- 2004

We give a O(√log n)-approximation algorithm for <sc>sparsest cut</sc>, <sc>balanced separator</sc>, and <sc>graph conductance</sc> problems. This improves the O(log n)-approximation of Leighton and Rao (1988). We use a well-known semidefinite relaxation with triangle inequality constraints. Central to our analysis is a geometric theorem aboutâ€¦ (More)

- Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, Mario Szegedy
- FOCS
- 1992

The class PCP(f(n), g(n)) consists of all languages L for which there exists a polynomial-time probabilistic oracle machine that uses O(f(n)) random bits, queries O(g(n)) bits of its oracle and behaves as follows: If x âˆˆ L then there exists an oracle y such that the machine accepts for all random choices but if x 6âˆˆ L then for every oracle y the machineâ€¦ (More)

- Sanjeev Arora, Elad Hazan, Satyen Kale
- Theory of Computing
- 2012

Algorithms in varied fields use the idea of maintaining a distribution over a certain set and use the multiplicative update rule to iteratively change these weights. Their analysis are usually very similar and rely on an exponential potential function. We present a simple meta algorithm that unifies these disparate algorithms and drives them as simpleâ€¦ (More)

- Sanjeev Arora
- 1993

We prove the following about the Nearest Lattice Vector Problem (in any`p norm), the Nearest Codeword Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NP-hard. 2. If for some > 0 there exists a polynomial-time algorithm thatâ€¦ (More)

- Sanjeev Arora, Rong Ge, +5 authors Michael Z L Zhu
- ICML
- 2013

Topic models provide a useful method for dimensionality reduction and exploratory data analysis in large text corpora. Most approaches to topic model learning have been based on a maximum likelihood objective. Efficient algorithms exist that attempt to approximate this objective, but they have no provable guarantees. Recently, algorithms have beenâ€¦ (More)