What question did this study set out to answer?

Design improved polynomial-time approximation algorithms with enhanced performance guarantees for fundamental NP-hard combinatorial optimization problems, specifically MAX CUT and MAX 2SAT.

November 1, 1995Journal of the ACMOpen Access

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

View Full Paper

Ask AI

Bookmark

Authors

MGMichel X. GoemansAgency for Science, Technology and Research DWDavid P. WilliamsonCornell University

Discussion

Member takes

Implication

Algorithmic analysis demonstrates 0.878-approximation guarantees for maximum cut and 2-satisfiability via semidefinite programming relaxations, suggesting new paradigms for combinatorial optimization.

Key Points

Design improved polynomial-time approximation algorithms with enhanced performance guarantees for fundamental NP-hard combinatorial optimization problems, specifically MAX CUT and MAX 2SAT.
Formulated continuous nonlinear relaxations of discrete optimization problems solvable as semidefinite programs or eigenvalue minimization tasks.
Introduced a randomized rounding technique using random hyperplanes to convert multidimensional vector solutions into discrete binary choices.
Extended the geometric relaxation and rounding framework to evaluate maximum directed cut (MAX DICUT) and general MAX SAT instances.
Achieved a proven expected approximation ratio of at least 0.87856 times the optimal value for both MAX CUT and MAX 2SAT, breaking a nearly 20-year stagnation.
Delivered improved approximation ratios of 0.79607 for MAX DICUT and 0.758 for general MAX SAT instances.
Established semidefinite programming as a viable and powerful algorithmic framework for approximating NP-hard optimization challenges.

Cite This Study

Goemans et al. (1995) studied this question.

synapsesocial.com/papers/69d9084cf544bba627bee0ef https://doi.org/10.1145/227683.227684

View Full Paper

Ask AI

Bookmark

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

Discussion

Member takes

Implication

Key Points

Cite This Study

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider