Arora, Sanjeev
Overview
Works:  18 works in 67 publications in 2 languages and 951 library holdings 

Genres:  Conference papers and proceedings Academic theses 
Roles:  Author, Editor, Creator 
Classifications:  QA75.5, 511.352 
Publication Timeline
.
Most widely held works by
Sanjeev Arora
Computational complexity : a modern approach by
Sanjeev Arora(
Book
)
21 editions published between 2008 and 2012 in English and Undetermined and held by 366 WorldCat member libraries worldwide
This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. The book starts with a broad introduction to the field and progresses to advanced results
21 editions published between 2008 and 2012 in English and Undetermined and held by 366 WorldCat member libraries worldwide
This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. The book starts with a broad introduction to the field and progresses to advanced results
Approximation, randomization, and combinatorial optimization : algorithms and techniques : 6th International Workshop on Approximation
Algorithms for Combinatorial Optimization Problems, APPROX 2003, and 7th International Workshop on Randomization and Approximation
Techniques in Computer Science, RANDOM 2003, Princeton, NJ, USA, August 2426, 2003 : proceedings by
Sanjeev Arora(
Book
)
18 editions published in 2003 in English and held by 234 WorldCat member libraries worldwide
This book constitutes the joint refereed proceedings of the 6th International Workshop on Approximation Algorithms for Optimization Problems, APPROX 2003 and of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, held in Princeton, NY, USA in August 2003. The 33 revised full papers presented were carefully reviewed and selected from 74 submissions. Among the issues addressed are design and analysis of randomized and approximation algorithms, online algorithms, complexity theory, combinatorial structures, errorcorrecting codes, pseudorandomness, derandomization, network algorithms, random walks, Markov chains, probabilistic proof systems, computational learning, randomness in cryptography, and various applications
18 editions published in 2003 in English and held by 234 WorldCat member libraries worldwide
This book constitutes the joint refereed proceedings of the 6th International Workshop on Approximation Algorithms for Optimization Problems, APPROX 2003 and of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, held in Princeton, NY, USA in August 2003. The 33 revised full papers presented were carefully reviewed and selected from 74 submissions. Among the issues addressed are design and analysis of randomized and approximation algorithms, online algorithms, complexity theory, combinatorial structures, errorcorrecting codes, pseudorandomness, derandomization, network algorithms, random walks, Markov chains, probabilistic proof systems, computational learning, randomness in cryptography, and various applications
Probabilistic checking of proofs and hardness of approximation problems by
Sanjeev Arora(
)
4 editions published in 1994 in English and held by 11 WorldCat member libraries worldwide
This dissertation establishes a surprising new characterization of NP, the class of languages for which membership proofs can be checked in polynomial time deterministically. The class NP is exactly the set of languages for which membership proofs can be checked by a probabilistic polynomial time verifier that examines a constant number of bits in the proof, and uses O(log n) random bits, where n is the size of the input
4 editions published in 1994 in English and held by 11 WorldCat member libraries worldwide
This dissertation establishes a surprising new characterization of NP, the class of languages for which membership proofs can be checked in polynomial time deterministically. The class NP is exactly the set of languages for which membership proofs can be checked by a probabilistic polynomial time verifier that examines a constant number of bits in the proof, and uses O(log n) random bits, where n is the size of the input
Approximation, randomization, and combinatorial optimization : algorithms and techniques ; 6th International Workshop on Approximation
Algorithms for Combinatorial Optimization Problems, and 7th International Workshop on Randomization and Approximation Techniques
in Computer Science, Princeton, NJ, USA, August 24  26, 2003 ; proceedings(
)
1 edition published in 2003 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 2003 in English and held by 8 WorldCat member libraries worldwide
Improved lowdegree testing and its applications by
Sanjeev Arora(
Book
)
3 editions published in 1997 in English and held by 7 WorldCat member libraries worldwide
Abstract: "NP=PCP(log n, 1) and related results crucially depend upon the close connection between the probability with which a function passes a low degree test and the distance of this function to the nearest degree d polynomial. In this paper we study a test proposed by Rubinfeld and Sudan [RS93]. The strongest previously known connection for this test states that a function passes the test with probability [delta] for some [delta]> 7/8 iff the function has agreement [symbol] [delta] with a polynomial of degree d. We present a new, and surprisingly strong, analysis which shows that the preceding statement is true for [delta] <<0.5. The analysis uses a version of Hilbert irreducibility, a tool of algebraic geometry. As a consequence we obtain an alternate construction for the following proof system: A constant prover 1round proof system for NP languages in which the verifier uses O(log n) random bits, receives answers of size O(log n) bits, and has an error probability of at most [formula]. Such a proof system, which implies the NPhardness of approximating Set Cover to within [omega](log n) factors, has already been obtained by Raz and Safra [RazS96]. Our result was completed after we heard of their claim. A second consequence of our analysis is a self tester/corrector for any buggy program that (supposedly) computes a polynomial over a finite field. If the program is correct only on [delta] fraction of inputs where [delta] = 1/[absolute value of F][superscript epsilon] <<0.5, then the tester/corrector determines [delta] and generates O(1/[delta]) values for every input, such that one of them is the correct output. In fact, our techniques yield something stronger: Given the buggy program, we can construct O(1/[delta]) randomized programs such that one of them is correct on every input, with high probability."
3 editions published in 1997 in English and held by 7 WorldCat member libraries worldwide
Abstract: "NP=PCP(log n, 1) and related results crucially depend upon the close connection between the probability with which a function passes a low degree test and the distance of this function to the nearest degree d polynomial. In this paper we study a test proposed by Rubinfeld and Sudan [RS93]. The strongest previously known connection for this test states that a function passes the test with probability [delta] for some [delta]> 7/8 iff the function has agreement [symbol] [delta] with a polynomial of degree d. We present a new, and surprisingly strong, analysis which shows that the preceding statement is true for [delta] <<0.5. The analysis uses a version of Hilbert irreducibility, a tool of algebraic geometry. As a consequence we obtain an alternate construction for the following proof system: A constant prover 1round proof system for NP languages in which the verifier uses O(log n) random bits, receives answers of size O(log n) bits, and has an error probability of at most [formula]. Such a proof system, which implies the NPhardness of approximating Set Cover to within [omega](log n) factors, has already been obtained by Raz and Safra [RazS96]. Our result was completed after we heard of their claim. A second consequence of our analysis is a self tester/corrector for any buggy program that (supposedly) computes a polynomial over a finite field. If the program is correct only on [delta] fraction of inputs where [delta] = 1/[absolute value of F][superscript epsilon] <<0.5, then the tester/corrector determines [delta] and generates O(1/[delta]) values for every input, such that one of them is the correct output. In fact, our techniques yield something stronger: Given the buggy program, we can construct O(1/[delta]) randomized programs such that one of them is correct on every input, with high probability."
Approximation schemes for the kmedians and related problems by
Sanjeev Arora(
Book
)
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Abstract: "In the kmedian problem we are given a set S of n points in a metric space and a positive integer k. We desire to locate k medians in space, such that the sum of the distances from each of the points of S to the nearest median is minimized. This paper gives an approximation scheme for the plane that for any c> 0 produces a solution of cost at most 1+1/c times the optimum and runs in time O(n[superscript O(c+1)]). The approximation scheme also generalizes to some problems related to kmedian. Our methodology is to extend Arora's [1, 2] techniques for TSP, which hitherto seemed inapplicable to problems such as the kmedian problem."
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Abstract: "In the kmedian problem we are given a set S of n points in a metric space and a positive integer k. We desire to locate k medians in space, such that the sum of the distances from each of the points of S to the nearest median is minimized. This paper gives an approximation scheme for the plane that for any c> 0 produces a solution of cost at most 1+1/c times the optimum and runs in time O(n[superscript O(c+1)]). The approximation scheme also generalizes to some problems related to kmedian. Our methodology is to extend Arora's [1, 2] techniques for TSP, which hitherto seemed inapplicable to problems such as the kmedian problem."
Polynomial time approximation schemes for dense instances of NPhard problems by
Sanjeev Arora(
Book
)
4 editions published between 1994 and 1998 in German and English and held by 5 WorldCat member libraries worldwide
4 editions published between 1994 and 1998 in German and English and held by 5 WorldCat member libraries worldwide
A Study of Privacy and Fairness in Sensitive Data Analysis by Moritz A. W Hardt(
Book
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
One important goal is to protect the privacy of those individuals whose personal information contributed to the data set. We consider algorithms that satisfy the strong privacy guarantee known as differential privacy. A wide range of computational tasks reduces to the setting in which a trusted database curator responds to a number of statistical queries posed by an untrusted data analyst. The basic question is how accurately and efficiently the curator can release approximate answers to the given queries while satisfying differential privacy. We make the following main contributions to differentially private data analysis
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
One important goal is to protect the privacy of those individuals whose personal information contributed to the data set. We consider algorithms that satisfy the strong privacy guarantee known as differential privacy. A wide range of computational tasks reduces to the setting in which a trusted database curator responds to a number of statistical queries posed by an untrusted data analyst. The basic question is how accurately and efficiently the curator can release approximate answers to the given queries while satisfying differential privacy. We make the following main contributions to differentially private data analysis
An investigation of a possible molecular effect in ion atom collisions using a gaseous argon target by
Sanjeev Arora(
)
2 editions published in 1992 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 2 WorldCat member libraries worldwide
Proof verification and the hardness of approximation problems(
Book
)
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
Abstract: "The class PCP(r(n), q(n)) consists of all languages L for which there exists a polynomialtime probabilistic oracle machine that uses O(r(n)) random bits, queries O(q(n)) bits of its oracle and behaves as follows: If x [member of] L then there exists an oracle y such that the machine accepts for all random choices but if x [not member of] L then for every oracle y the machine rejects with high probability. Arora and Safra very recently characterized NP as PCP(log n, (log log n)[superscript O(1)]). We improve on their result by showing that NP = PCP(log n, 1). Our result has the following consequences: 1. MAXSNPhard problems (e.g., metric TSP, MAXSAT, MAXCUT) do not have polynomial time approximation schemes unles P=NP. 2. For some [epsilon]> 0 the size of the maximal clique in a graph cannot be approximated within a factor of n[superscript [epsilon]] unless P=NP."
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
Abstract: "The class PCP(r(n), q(n)) consists of all languages L for which there exists a polynomialtime probabilistic oracle machine that uses O(r(n)) random bits, queries O(q(n)) bits of its oracle and behaves as follows: If x [member of] L then there exists an oracle y such that the machine accepts for all random choices but if x [not member of] L then for every oracle y the machine rejects with high probability. Arora and Safra very recently characterized NP as PCP(log n, (log log n)[superscript O(1)]). We improve on their result by showing that NP = PCP(log n, 1). Our result has the following consequences: 1. MAXSNPhard problems (e.g., metric TSP, MAXSAT, MAXCUT) do not have polynomial time approximation schemes unles P=NP. 2. For some [epsilon]> 0 the size of the maximal clique in a graph cannot be approximated within a factor of n[superscript [epsilon]] unless P=NP."
Approximation, randomization, and combinatorial optimization : algorithms and techniques : 7th International Workshop on Approximation
Algorithms for Combinatorial Optimization Problems, APPROX 2004, and 8th International Workshop on Randomization and Computation,
RANDOM 2004, Cambridge, MA, USA, August 2224, 2004 : proceedings by
Anupam Gupta(
)
2 editions published in 2003 in English and held by 2 WorldCat member libraries worldwide
This book constitutes the joint refereed proceedings of the 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2004 and the 8th International Workshop on Randomization and Computation, RANDOM 2004, held in Cambridge, MA, USA in August 2004. The 37 revised full papers presented were carefully reviewed and selected from 87 submissions. Among the issues addressed are design and analysis of approximation algorithms, inapproximability results, approximation classes, online problems, graph algorithms, cuts, geometric computations, network design and routing, packing and covering, scheduling, game theory, design and analysis of randomised algorithms, randomized complexity theory, pseudorandomness, derandomization, probabilistic proof systems, errorcorrecting codes, and other applications of approximation and randomness
2 editions published in 2003 in English and held by 2 WorldCat member libraries worldwide
This book constitutes the joint refereed proceedings of the 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2004 and the 8th International Workshop on Randomization and Computation, RANDOM 2004, held in Cambridge, MA, USA in August 2004. The 37 revised full papers presented were carefully reviewed and selected from 87 submissions. Among the issues addressed are design and analysis of approximation algorithms, inapproximability results, approximation classes, online problems, graph algorithms, cuts, geometric computations, network design and routing, packing and covering, scheduling, game theory, design and analysis of randomised algorithms, randomized complexity theory, pseudorandomness, derandomization, probabilistic proof systems, errorcorrecting codes, and other applications of approximation and randomness
Online algorithms for path selection in nonblocking networks by
Sanjeev Arora(
Book
)
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
Hardness of approximations by
Sanjeev Arora(
)
1 edition published in 1997 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1997 in English and held by 2 WorldCat member libraries worldwide
On winning strategies in EhrenfeuchtFraiesse games by
Thomas J. Watson IBM Research Center(
Book
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
A polynomialtime approximation scheme for weighted planar graph TSP(
)
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
Page replacement for general caching problems by
Susanne Albers(
)
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
A (2 + [...])approximation algorithm for the kMST problem by
Sanjeev Arora(
)
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
A new calculation of the antiproton to proton ratio in supernova shells by
Sanjeev Arora(
)
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Barak, Boaz
 Jansen, Klaus
 Sahai, Amit
 Rolim, José D. P.
 International Workshop on Approximation Algorithms for Combinatorial Optimization Problems 2003 Princeton, NJ
 Barak, Boaz
 International Workshop on Randomization and Approximation Techniques in Computer Science 2003 Princeton, NJ
 Raghavan, Prabhakar
 Rao, Satish
 Sudan, Madhu
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Associated Subjects
Algorithms Antiprotons Combinatorial analysis Combinatorial optimization Computational complexity Computer algorithms Computer science Computer scienceMathematics Computer scienceStatistical methods Computer software Computer vision Electronic data processing Geometry, Algebraic Irreducible polynomials Mathematical optimization Programming (Mathematics) Protons Supernovae Traveling salesman problem University of California, Berkeley.Computer Science Division