Private approximation of search problems

Amos Beimel, Paz Carmi, Kobbi Nissim, Enav Weinreb

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

16 Scopus citations


Many approximation algorithms have been presented in the last decades for hard search problems. The focus of this paper is on cryptographic applications, where it is desired to design algorithms which do not leak unnecessary information. Specifically, we are interested in private approximation algorithms - efficient algorithms whose output does not leak information not implied by the optimal solutions to the search problems. Privacy requirements add constraints on the approximation algorithms; in particular, known approximation algorithms usually leak a lot of information. For functions, [Feigenbaum et al., ICALP 2001] presented a natural requirement that a private algorithm should not leak information not implied by the original function. Generalizing this requirement to search problems is not straightforward as an input may have many different outputs. We present a new definition that captures a minimal privacy requirement from such algorithms - applied to an input instance, it should not leak any information that is not implied by its collection of exact solutions. Although our privacy requirement seems minimal, we show that for well studied problems, as vertex cover and max exact 3SAT, private approximation algorithms are unlikely to exist even for poor approximation ratios. Similar to [Halevi et al., STOC 2001], we define a relaxed notion of approximation algorithms that leak (little) information, and demonstrate the applicability of this notion by showing near optimal approximation algorithms for max exact 3SAT that leak little information.

Original languageEnglish
Title of host publicationSTOC'06
Subtitle of host publicationProceedings of the 38th Annual ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Number of pages10
ISBN (Print)1595931341, 9781595931344
StatePublished - 1 Jan 2006
Event38th Annual ACM Symposium on Theory of Computing, STOC'06 - Seattle, WA, United States
Duration: 21 May 200623 May 2006

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference38th Annual ACM Symposium on Theory of Computing, STOC'06
Country/TerritoryUnited States
CitySeattle, WA


  • Algorithms
  • Theory

ASJC Scopus subject areas

  • Software


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