We present a simple family of algorithms for solving the Generalized Assignment Problem (GAP). Our technique is based on a novel combinatorial translation of any algorithm for the knapsack problem into an approximation algorithm for GAP. If the approximation ratio of the knapsack algorithm is α and its running time is O(f (N )), our algorithm guarantees a (1 + α)-approximation ratio, and it runs in O(M · f (N) + M · N), where N is the number of items and M is the number of bins. Not only does our technique comprise a general interesting framework for the GAP problem; it also matches the best combinatorial approximation for this problem, with a much simpler algorithm and a better running time.
A (2 + ε)-approximation algorithm with the same guarantee as the combinatorial local search but a better running time is given in REF .
An efficient approximation for the Generalized Assignment Problem
Information Processing Letters
Information Processing Letters
Mathematics Computer Science