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Playing "Hide-and-Seek" in Finite Fields: The Hidden Number.. - Shparlinski (2002) (Correct)
....the algorithm of [53] requires . We also mention that the Poly HNP is related to several other polynomial interpolation and approximation problems. In particular, it has links with noisy polynomial interpolation [5, 24, 52, 61] learning and reconstructing polynomials with noisy queries [2, 3, 18, 30] and sparse polynomial interpolation [13, 22, 33, 62, 63] 11 10 HNP over Unknown Algebraic Number Fields ANF HNP A HNP of a di#erent spirit has recently been introduced and studied in [57] To describe this problem we need to recall some basic facts of the theory of algebraic number ....
S. Arora and M. Sudan, `Improved low-degree testing and its applications ', Proc. 29nd ACM Symp. on Theory of Comp., (1997), 485--495.
Approximation Algorithms For Terrain Guarding - Eidenbenz (2002) (1 citation) (Correct)
.... SET COVER, which consists of recursively adding to the solution a set that contains a maximum number of elements not yet covered by the current solution, achieves an approximation ratio of ln n 1 [11] It turns out that this approximation algorithm is the best possible (up to low order terms) [1,9]. There are several surveys on art galleries [14 16] Many upper and lower bounds on the number of necessary guards are known for different guarding problems, while comparatively few results are known on the computational complexity of these guarding problems. It is known that guarding a given ....
S. Arora, M. Sudan, Improved low-degree testing and its applications, in: Proc. 29th ACM Symposium on the Theory of Computing, El Paso, TX, 1997, pp. 485--495.
Budget Constrained Minimum Cost Connected Medians - Konjevod, Krumke, Marathe (Correct)
....problem for graphs that are simultaneously of bounded treewidth, planar and of bounded degree. Next, we give inapproximability results for general graphs. Before stating the hardness result we recall the definition of the MIN SET COVER problem [12, Problem SP5] and cite the hardness results from [11, 4] about the hardness of approximating MIN SET COVER. An instance (U; S) of MIN SET COVER consists of a finite set U of ground elements and a family S of subsets of U . The objective is to find a subcollection C S of minimum size jCj which contains all the ground elements. THEOREM 5.2 (Feige ....
....minimum size jCj which contains all the ground elements. THEOREM 5.2 (Feige [11] Unless NP DTIME(N O(log log N) for any 0 there is no approximation algorithm for MIN SET COVER with a performance of (1 ) ln jU j, where U is the set of ground elements. THEOREM 5. 3 (Arora and Sudan [4]) There exists a constant 0 such that, unless P = NP, there is no approximation algorithm for MIN SET COVER with a performance of ln jU j, where U is the set of ground elements. We are now ready to prove the result about the inapproximability of BCCMED on general graphs. THEOREM 5.4 The ....
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S. Arora and M. Sudan. Improved low-degree testing and its applications. In Proceedings of the 29th Annual ACM Symposium on the Theory of Computing, pages 485--496, 1997.
The art of uninformed decisions: A primer to property testing - Fischer (2001) (10 citations) (Correct)
....: F F being a polynomial of a total degree bounded by k can be tested using O(k k ) queries (independently of jF j and d) There was extensive research in the topic of testing a function for being a low degree polynomial, and related questions. The interested reader is referred to [7], that describes some additional results. 3 Testing of languages As the possibility of testing an input for a property using few queries becomes apparent, the next natural step is to correlate the traditional categorization of properties into complexity classes with this new scheme. An ultimate ....
S. Arora and M. Sudan, Improved low-degree testing and its applications, Proceedings of the ACM STOC (1997), 485-495.
Randomness-efficient Low Degree Tests and Short PCPs via.. - Ben-Sasson, Sudan, al. Self-citation (Sudan) (Correct)
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S. Arora and M. Sudan. Improved low degree testing and its applications. In 29th STOC, pages 485--495, 1997.
Randomness-efficient Low Degree Tests and Short PCPs via.. - Ben-Sasson, Sudan, al. (2003) Self-citation (Sudan) (Correct)
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S. Arora and M. Sudan. Improved low degree testing and its applications. In 29th STOC, pages 485--495, 1997.
Lecturer: Madhu Sudan Scribe: Ryan O'Donnell - Error Correcting Codes Self-citation (Sudan) (Correct)
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Sanjeev Arora and Madhu Sudan. Improved low-degree testing and its applications. In Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pages 485-495, El Paso, Texas, 4-6 May 1997.
Locally Testable Codes and PCPs of almost-Linear Length - Goldreich, Sudan (2004) (3 citations) Self-citation (Sudan) (Correct)
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S. Arora and M. Sudan. Improved low degree testing and its applications. In 29th STOC, pages 485--495, 1997.
The Approximability of Constraint Satisfaction Problems - Khanna, Sudan, Trevisan.. (2001) (6 citations) Self-citation (Sudan) (Correct)
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S. Arora and M. Sudan, Improved low degree testing and its applications, in Proceedings of the 29th Annual ACM Symposium on Theory of Computing, El Paso, TX, 1997, pp. 485--495.
Robust Locally Testable Codes and Products of Codes - Ben-Sasson, Sudan (2004) Self-citation (Sudan) (Correct)
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Sanjeev Arora and Madhu Sudan. Improved low-degree testing and its applications. In Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pages 485--495, El Paso, Texas, 4-6 May 1997.
Locally Testable Codes and PCPs of Almost-Linear Length - Preliminary Version Oded Self-citation (Sudan) (Correct)
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S. Arora and M. Sudan. Improved low degree testing and its applications. In 29th STOC, pages 485--495, 1997.
Reflections on "Improved Decoding of Reed-Solomon.. - Guruswami, Sudan (2002) Self-citation (Sudan) (Correct)
....of Reed Muller codes. The technique used in [23] unfortunately does not seem to generalize in any simple way to decode Reed Muller codes up to their list decoding radius, or for that matter even beyond half the distance for all rates, and this remains an interesting open question. However, in [2, 40], using clever reductions to the univariate case, an algorithm to list decode Reed Muller codes well beyond half the distance is presented for codes of low rate. A consequence of Theorem 2 is that, for arbitrary 0, ecient list decoding up to a fraction (1 ) of errors can be performed using ....
Sanjeev Arora and Madhu Sudan. Improved low-degree testing and its applications. In Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pages 485-495, El Paso, Texas, 4-6 May 1997.
Locally Testable Codes and PCPs of Almost-Linear Length - Goldreich, Sudan (2002) (3 citations) Self-citation (Sudan) (Correct)
....larger prover to roughly the size of the smaller prover. We then show how to apply the random truncation to the veri er of a speci c 3 prover one round proof system used by Harsha and Sudan [15] Their veri er is a variant of the one constructed by Raz and Safra [18] see also, Arora and Sudan [3]) which are, in turn, variants of a veri er constructed by Arora et al. 1] All these veri ers share the common property of working with provers of imbalanced sizes. We manage to reduce the size of the provers to the size of the smallest one, and consequently reduce the randomness of the ....
....at least , it maps unsatis able instances of SAT to no instances of . 4.3 Nearly linear PCPs Applying state of the art composition lemmas to the MIP constructed in the previous subsection gives our nal results quite easily. In particular, we use the following lemmas. Lemma 4. 13 (cf. [3] or [5, 18] For every 1 0 and p 1, there exists 0 and constants c 1 ; c 2 ; c 3 such that for every r; a : Z MIP 1; p; r; a] MIP 1; 1 [p 3; r c 1 log a; c 2 (log a) We apply the lemma above repeatedly till the answer lengths become poly log log log n. Then to ....
S. Arora and M. Sudan. Improved low degree testing and its applications. In 29th STOC, pages 485-495, 1997.
Inapproximability of Some Art Gallery Problems - Eidenbenz, Stamm, Widmayer (1998) (Correct)
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S. Arora and M. Sudan; Improved low-degree testing and its applications; Proc. STOC '97, pp. 485 - 495, 1997.
Nonuniform Hard Boolean Functions and Uniform Complexity Classes - Kabanets (2001) (Correct)
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S. Arora and M. Sudan. Improved low-degree testing and its applications. In Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pages 485-495, 1997.
Property Testing - Ron (2000) (16 citations) (Correct)
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S. Arora and S. Sudan. Improved low degree testing and its applications. In Proceedings of the Thirty-First Annual ACM Symposium on the Theory of Computing, pages 485-- 495, 1997.
Inapproximability of Some Art Gallery Problems - Eidenbenz, Stamm, Widmayer (1998) (Correct)
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S. Arora and M. Sudan; Improved low-degree testing and its applications; Proc. STOC '97, pp. 485 - 495, 1997.
Monotonicity Testing - Raskhodnikova (1999) (Correct)
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S. Arora and S. Sudan. Improved low degree testing and its applications. In Proceedings of STOC97, pages 485-495, 1997.
Some Applications of Coding Theory in Computational Complexity - Trevisan (2004) (Correct)
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S. Arora and M. Sudan. Improved low degree testing and its applications. In Proceedings of the 29th ACM Symposium on Theory of Computing, pages 485--495, 1997.
Polynomial Factorization: a Success Story - Kaltofen (Correct)
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S. Arora and M. Sudan. Improved low degree testing and its applications. In Proc. 29th Annual ACM Symp. Theory Comput., pages 485--495, New York, N.Y., 1997. ACM Press. Full version available from http://theory.lcs.mit.edu/ # madhu/papers.html.
The Computational Complexity Column - Lance Fortnow Nec (Correct)
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S. Arora and M. Sudan. Improved low-degree testing and its applications. In Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pages 485-495, 1997.
Improved Approximation Algorithms for - Capacitated Facility Location (Correct)
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S. Arora and M. Sudan. Improved low-degree testing and its applications. In Proceedings of the 29th ACM Symposium on Theory of Computing, pages 485--495, 1997.
Distribution-Free Property Testing - Halevy, Kushilevitz (Correct)
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S. Arora and M. Sudan, Improved low-degree testing and its applications. Proceedings ACM STOC 485--495,1997.
Testing Low-Degree Polynomials over GF(2) - Alon, Kaufman, Krivelevich.. (2003) (4 citations) (Correct)
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S. Arora and S. Safra. Improved low-degree testing and its applications. In Proceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing, pages 485--495, 1997.
Testing Low-Degree Polynomials over GF(2) - Alon, Kaufman, Krivelevich.. (2003) (4 citations) (Correct)
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S. Arora and S. Safra. Improved low-degree testing and its applications. In Proceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing, pages 485--495, 1997.
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