# Approximation Algorithms

### Some articles on approximation algorithms, approximation algorithm, approximation, algorithm:

Maximum Cut - Approximation Algorithms
... Thus, every polynomial-time approximation algorithm achieves an approximation ratio strictly less than one ... There is a simple randomized 0.5-approximation algorithm for each vertex flip a coin to decide to which half of the partition to assign it ... This algorithm can be derandomized with the method of conditional probabilities therefore there is a simple deterministic polynomial-time 0.5-approximati ...
Travelling Salesman Problem - Computing A Solution - Special Cases - Metric TSP
... in terms of the minimum spanning tree and design an algorithm that has a provable upper bound on the length of the route ... The Christofides algorithm follows a similar outline but combines the minimum spanning tree with a solution of another problem, minimum-weight perfect ... The Christofides algorithm was one of the first approximation algorithms, and was in part responsible for drawing attention to approximation algorithms as a practical approach to ...
Linear Programming Relaxation - Approximation and Integrality Gap
... Linear programming relaxation is a standard technique for designing approximation algorithms for hard optimization problems ... Typically, this gap translates into the approximation ratio of an approximation algorithm ... As Young (1995) showed, both the random part of this algorithm and the need to construct an explicit solution to the linear programming relaxation may be eliminated using the method of ...
Planar Separator Theorem - Applications - Approximation Algorithms
... observed that the separator theorem may be used to obtain polynomial time approximation schemes for NP-hard optimization problems on planar graphs such as finding the ... However, for approximation ratios even closer to 1 than this factor, a later approach of Baker (1994) (based on tree-decomposition but not on planar separators) provides better tradeoffs of ... Similar separator-based approximation schemes have also been used to approximate other hard problems such as vertex cover ...