Improved approximation algorithms for multidimensional bin packing problems

In this paper we introduce a new general framework for set covering problems, based on the combination of randomized rounding of the (near-)optimal solution of the Linear Programming (LP) relaxation, leading to a partial integer solution, and the application of a well-behaved approximation algorithm to complete this solution. If the value of the solution returned by the latter can be bounded in a suitable way, as is the case for the most relevant generalizations of bin packing, the method leads to improved approximation guarantees, along with a proof of tighter integrality gaps for the LP relaxation. Applying our general framework we obtain a polynomial-time randomized algorithm for d-dimensional vector packing with approximation guarantee arbitrarily

• Type: Conference
• Year: 2006
• Where: FOCS
• Authors: Nikhil Bansal, Alberto Caprara, Maxim Sviridenko
• Keywords: Approximation Guarantee, FOCS 2006, General Framework, Theoretical Computer Science, Well-behaved Approximation Algorithm