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Sublineartime algorithms
 In Oded Goldreich, editor, Property Testing, volume 6390 of Lecture Notes in Computer Science
, 2010
"... In this paper we survey recent (up to end of 2009) advances in the area of sublineartime algorithms. 1 ..."
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Cited by 12 (3 self)
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In this paper we survey recent (up to end of 2009) advances in the area of sublineartime algorithms. 1
New Sublinear Methods in the Struggle against Classical Problems
, 2010
"... We study the time and query complexity of approximation algorithms that access only a minuscule fraction of the input, focusing on two classical sources of problems: combinatorial graph optimization and manipulation of strings. The tools we develop find applications outside of the area of sublinear ..."
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Cited by 2 (0 self)
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We study the time and query complexity of approximation algorithms that access only a minuscule fraction of the input, focusing on two classical sources of problems: combinatorial graph optimization and manipulation of strings. The tools we develop find applications outside of the area of sublinear algorithms. For instance, we obtain a more efficient approximation algorithm for edit distance and distributed algorithms for combinatorial problems on graphs that run in a constant number of communication rounds.
ConstantTime Approximation . . .
"... We present a technique for transforming classical approximation algorithms into constanttime algorithms that approximate the size of the optimal solution. Our technique is applicable to a certain subclass of algorithms that compute a solution in a constant number of phases. The technique is based o ..."
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We present a technique for transforming classical approximation algorithms into constanttime algorithms that approximate the size of the optimal solution. Our technique is applicable to a certain subclass of algorithms that compute a solution in a constant number of phases. The technique is based on greedily considering local improvements in random order. The problems amenable to our technique include
Sequence Comparison
"... ensuring compliance with copyright. For more information, please contact scholarworks@uno.edu. Robust and Efficient Algorithms for Protein 3D Structure Alignment and Genome ..."
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ensuring compliance with copyright. For more information, please contact scholarworks@uno.edu. Robust and Efficient Algorithms for Protein 3D Structure Alignment and Genome
Electronic Colloquium on Computational Complexity, Report No. 94 (2005) On Approximating the Minimum Vertex Cover in Sublinear Time and the Connection to Distributed Algorithms
"... We consider the problem of estimating the size, V C(G), of a minimum vertex cover of a graph G, in sublinear time, by querying the incidence relation of the graph. We say that an algorithm is an (α, ɛ)approximation algorithm if it outputs with high probability an estimate V C such that V C(G) − ɛn ..."
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We consider the problem of estimating the size, V C(G), of a minimum vertex cover of a graph G, in sublinear time, by querying the incidence relation of the graph. We say that an algorithm is an (α, ɛ)approximation algorithm if it outputs with high probability an estimate V C such that V C(G) − ɛn ≤ V C ≤ α · V C(G) + ɛn, where n is the number of vertices of G. We show that the query complexity of such algorithms must grow at least linearly with the average degree ¯ d of the graph. In particular this means that for dense graphs it is not possible to design an algorithm whose complexity is o(n). On the positive side we first describe a simple (O(log ( ¯ d/ɛ), ɛ)approximation algorithm, whose query complexity is ɛ −2 · ( ¯ d/ɛ) log ( ¯ d/ɛ)+O(1) We then show a reduction from local distributed approximation algorithms to sublinear approximation algorithms. Using this reduction and the distributed algorithm of Kuhn, Moscibroda, and Wattenhofer [KMW05] we can get an (O(1), ɛ)approximation algorithm, whose query complexity is ɛ −2 · ( ¯ d/ɛ) O(log ( ¯ d/ɛ) ISSN 14338092