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Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
TLDR
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.
A general approximation technique for constrained forest problems
TLDR
The first approximation algorithms for many NP-complete problems, including the non-fixed point-to-point connection problem, the exact path partitioning problem and complex location-design problems are derived.
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
  • U. Feige, M. Goemans
  • Computer Science, Mathematics
    Proceedings Third Israel Symposium on the Theory…
  • 4 January 1995
TLDR
The approach combines the Feige-Lovasz (STOC92) semidefinite programming relaxation of one-round two-prover proof systems, together with rounding techniques for the solutions of semideFinite programs, as introduced by Goemans and Williamson (SToc94).
.879-approximation algorithms for MAX CUT and MAX 2SAT
TLDR
This research presents randomized approximation algorithms for the MAX CUT and MAX 2SAT problems that always deliver solutions of expected value at least .87856 times the optimal value and represents the first use of semidefinite programming in the design of approximation algorithms.
New 3/4-Approximation Algorithms for the Maximum Satisfiability Problem
TLDR
It is shown that although standard randomized rounding does not give a good approximate result, the best solution of the two given by randomized rounding and a well-known algorithm of Johnson is always within $\frac{3}{4}$ of the optimal solution.
Approximating submodular functions everywhere
TLDR
The problem of approximating a non-negative, monotone, submodular function f on a ground set of size n everywhere is considered, after only poly(n) oracle queries, and it is shown that no algorithm can achieve a factor better than Ω(√n/log n), even for rank functions of a matroid.
Semidefinite programming in combinatorial optimization
  • M. Goemans
  • Mathematics, Computer Science
    Math. Program.
  • 1 October 1997
TLDR
The main topics covered include the Lovász theta function and its applications to stable sets, perfect graphs, and coding theory, the automatic generation of strong valid inequalities, and the embedding of finite metric spaces.
The primal-dual method for approximation algorithms and its application to network design problems
TLDR
The primal-dual method was proposed by Dantzig, Ford, and Fulkerson [DFF56] as another means of solving linear programs, and Ironically, their inspiration came from combinatorial optimization.
An improved approximation ratio for the minimum latency problem
TLDR
The development of the algorithm involves a number of techniques that seem to be of interest from the perspective of the TSP and its variants more generally, and improves the approximation ratio to 21.55.
Sink equilibria and convergence
TLDR
It is argued that there is a natural convergence process to sink equilibria in games where agents use pure strategies, and the price of sinking is an alternative measure of the social cost of a lack of coordination, which measures the worst case ratio between thevalue of a sink equilibrium and the value of the socially optimal solution.
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