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## Private Approximation of Search Problems (2005)

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Venue: | ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY |

Citations: | 15 - 2 self |

### Citations

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Citation Context ...s a fraction of atleast 7/8 - ffl of the clauses in the formula. There are (ffl, 3)-wise independent spaces of size poly( log nffl ). Togenerate the assignments we can use any of the constructions of =-=[22, 2]-=-. 2 Claim 4.6 Every solution-list algorithm for maxE3SAT that achieves approximation ratio better than 1/2uses at least log n - 1 solutions. Proof: Assume a solution-list algorithm for maxE3SAT, and l... |

296 | Efficient private matching and set intersection
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Citation Context ...it strings with communicationcomplexity ~ O(pn), and polynomial solutions for approximating the permanent and other natural #P prob-lems. Other private approximation protocols published since include =-=[19, 9, 17]-=-. In particular, Indyk and Woodruff [17] provide a polylogarithmic communication approximation for the Hamming distance and asecure approximation of the near neighbor search problem. Inapproximability... |

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Citation Context ...ize O(n3),this implies the existence of the list. To generate the assignments we can use any of the constructions of 3-wise independent spaces, e.g., the construction based on polynomials (see, e.g., =-=[20, 1, 6]-=-).We next describe the (7/8 - ffl)-approximation algorithm. As in the previous case, it suffices to showhow to efficiently construct, for every n and ffl > 0, a list of poly( log nffl ) assignments su... |

174 |
A local-ratio theorem for approximating the weighted vertex cover problem
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(Show Context)
Citation Context ...ax exact 3SAT to nonprivate computation and privately approximating the size of the solutions. The vertex cover problem can be (non-privately) (2 − o(1))-approximated in deterministic polynomial time =-=[21, 4, 15]-=-, and if P �= N P, then there is no polynomial-time 1.3606-approximation algorithm for vertex cover [7]. In contrast, we show that if RP �= N P, then this problem cannot be privately n 1−ɛ -approximat... |

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Citation Context ...e O(n3 ), this implies the existence of the list. To generate the assignments we can use any of the constructions of 3-wise independent spaces, e.g., the construction based on polynomials (see, e.g., =-=[20, 1, 6]-=-). We next describe the (7/8 − ɛ)-approximation algorithm. As in the previous case, it suffices to show how to efficiently construct, for every n and ɛ > 0, a list of poly( log n ɛ ) assignments such ... |

113 | Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs. In: - Halperin - 2000 |

108 | Secure multiparty computation of approximations,
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Citation Context ...mation ˆ f. This raises the question of which approximation to use, as S is only willing to reveal f(G), but ˆ f may leak some other information. This was the setting in the work by Feigenbaum et al. =-=[8]-=-. They defined the notion of private approximation that combines two requirements: (i) approximation: ˆ f is an approximation to f, and (ii) functional privacy: ˆ f(G) can be simulated given f(G); In ... |

87 | On the hardness of approximating minimum vertex cover,
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(Show Context)
Citation Context ...er problem canbe (non-privately) (2 - o(1))-approximated in deterministic polynomial time [21, 4, 15], and if P 6= N P,then there is no polynomial-time 1.3606-approximation algorithm for vertex cover =-=[7]-=-. In contrast, weshow that if RP 6 = N P, then this problem cannot be privately n1-ffl-approximated (even if a leakage of log n bits is allowed). The max exact 3SAT problem can be 7/8-approximated [18... |

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Citation Context ...ratio). A similar relaxation of privacy is the notion of additional information in secure two-party protocols by Bar-Yehuda et al. [3]. Related ideas can be found in the study of knowledge complexity =-=[13, 12, 5, 11, 24]-=-. We next compare the possibility and impossibility results for vertex cover and max exact 3SAT to nonprivate computation and privately approximating the size of the solutions. The vertex cover proble... |

15 | Privacy, additional information, and communication
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Citation Context ...generally, there is a tradeoff between the leakage and approximation ratio). A similar relaxation of privacy is the notion of additional information in secure two-party protocols by Bar-Yehuda et al. =-=[3]-=-. Related ideas can be found in the study of knowledge complexity [13, 12, 5, 11, 24]. We next compare the possibility and impossibility results for vertex cover and max exact 3SAT to nonprivate compu... |

11 |
additional information and communication
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(Show Context)
Citation Context ... generally, there is a tradeoff between the leakage and approximation ratio). A similar relaxation of privacyis the notion of additional information in secure two-party protocols by Bar-Yehuda et al. =-=[3]-=-. Related ideas can be found in the study of knowledge complexity [13, 12, 5, 11, 24].We next compare the possibility and impossibility results for vertex cover and max exact 3SAT to nonprivate comput... |

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1 | Privateapproximation of search problems - Beimel, Carmi, et al. - 1992 |