Journal ArticleDOI
Some optimal inapproximability results
TLDR
It is proved optimal, up to an arbitrary ε > 0, inapproximability results for Max-E k-Sat for k ≥ 3, maximizing the number of satisfied linear equations in an over-determined system of linear equations modulo a prime p and Set Splitting.Abstract:
We prove optimal, up to an arbitrary e > 0, inapproximability results for Max-E k-Sat for k ≥ 3, maximizing the number of satisfied linear equations in an over-determined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds for the efficient approximability of many optimization problems studied previously. In particular, for Max-E2-Sat, Max-Cut, Max-di-Cut, and Vertex cover.read more
Citations
More filters
Proceedings ArticleDOI
Mechanism Design via Differential Privacy
Frank McSherry,Kunal Talwar +1 more
TL;DR: It is shown that the recent notion of differential privacv, in addition to its own intrinsic virtue, can ensure that participants have limited effect on the outcome of the mechanism, and as a consequence have limited incentive to lie.
Proceedings ArticleDOI
On the power of unique 2-prover 1-round games
TL;DR: The main idea is to use the 2-prover game given by the Unique Games Conjecture as an "outer verifier" and build new probabilistically checkable proof systems (PCPs) on top of it.
BookDOI
Complexity and Approximation
Giorgio Ausiello,Alberto Marchetti-Spaccamela,Pierluigi Crescenzi,Giorgio Gambosi,Marco Protasi,Viggo Kann +5 more
Journal ArticleDOI
Pseudo-boolean optimization
Endre Boros,Peter L. Hammer +1 more
TL;DR: This survey examines the state of the art of a variety of problems related to pseudo-Boolean optimization, i.e. to the optimization of set functions represented by closed algebraic expressions.
Book
Analysis of Boolean Functions
TL;DR: This text gives a thorough overview of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry, and includes a "highlight application" such as Arrow's theorem from economics.
References
More filters
Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Journal ArticleDOI
Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
TL;DR: This algorithm gives the first substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semidefinite programming in the design of approximation algorithms.
Journal ArticleDOI
A threshold of ln n for approximating set cover
TL;DR: It is proved that (1 - o(1) ln n setcover is a threshold below which setcover cannot be approximated efficiently, unless NP has slightlysuperpolynomial time algorithms.
Journal ArticleDOI
Approximation algorithms for combinatorial problems
TL;DR: For the problem of finding the maximum clique in a graph, no algorithm has been found for which the ratio does not grow at least as fast as n^@e, where n is the problem size and @e>0 depends on the algorithm.