Approximate modularity

Show simple item record Chierichetti, Flavio Das, Abhimanyu Dasgupta, Anirban Kumar, Ravi
dc.contributor.other 56th IEEE Annual Symposium on Foundations of Computer Science (FOCS)
dc.coverage.spatial Berkeley, US 2016-04-16T18:18:01Z 2016-04-16T18:18:01Z 2015-10-17
dc.identifier.citation Chierichetti, Flavio; Das, Abhimanyu; Dasgupta, Anirban and Kumar, Ravi, “Approximate modularity”, in the 56th IEEE Annual Symposium on Foundations of Computer Science (FOCS), Berkeley, US, Oct. 17-20, 2015. en_US
dc.description.abstract A set function on a ground set of size n is approximately modular if it satisfies every modularity requirement to within an additive error, approximate modularity is the set analog of approximate linearity. In this paper we study how close, in additive error, can approximately modular functions be to truly modular functions. We first obtain a polynomial time algorithm that makes O(n2 log n) queries to any approximately modular function to reconstruct a modular function that is O(√n)-close. We also show an almost matching lower bound: any algorithm world need super polynomially many queries to construct a modular function that is o(√(n/log n))-close. In a striking contrast to these near-tight computational reconstruction bounds, we then show that for any approximately modular function, there exists a modular function that is O(log n)-close. en_US
dc.description.statementofresponsibility by Flavio Chierichetti et al.
dc.language.iso en_US en_US
dc.publisher IEEE en_US
dc.subject Polynomials en_US
dc.subject Set theory en_US
dc.subject Additives en_US
dc.subject Approximation algorithms en_US
dc.subject Approximation methods en_US
dc.subject Linearity en_US
dc.subject Manganese en_US
dc.subject Polynomials en_US
dc.subject Yttrium en_US
dc.title Approximate modularity en_US
dc.type Article en_US

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