It is proved that no polynomial algorithm can achieve a worst-case ratio less than 3/2 unlessP = NP, and a complexity classification for all special cases with a fixed number of processing times is obtained.Expand

The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs. Each job is to be processed by exactly one machine; processing jobj on machinei… Expand

This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions to discrete optimization problems.Expand

A new approach to constructing approximation algorithms, which the aim is find superoptimal, but infeasible solutions, and the performance is measured by the degree of infeasibility allowed, which should find wide applicability for any optimization problem where traditional approximation algorithms have been particularly elusive.Expand

A polynomial-time algorithm is given that finds a solution of cost within a factor of 3.16 of the optimal for the uncapacitated facility location, which is the first constant performance guarantee known for this problem.Expand

The techniques developed in this paper greatly outperform the general methods in many applications, and are extensions of a method previously applied to find approximate solutions to multicommodity flow problems.Expand

A 2-approximation algorithm for the k-center problem with triangle inequality is presented, the key combinatorial object used is called a strong stable set, and the NP-completeness of the corresponding decision problem is proved.Expand

This survey focuses on the area of deterministic machine scheduling, and reviews complexity results and optimization and approximation algorithms for problems involving a single machine, parallel machines, open shops, flow shops and job shops.Expand

This work develops an adaptive policy that learns the unknown parameters from past data and at the same time optimizes the profit and develops a simple algorithm for computing a profit-maximizing assortment based on the geometry of lines in the plane.Expand

A (1+2/e)-approximation algorithm is obtained, which is a significant improvement on the previously known approximation guarantees, and works by rounding an optimal fractional solution to a linear programming relaxation.Expand