A General Framework for Designing Approximation Schemes for Combinatorial Optimization Problems with Many Objectives Combined into One

Authors:
Shashi Mittal;Andreas S. Schulz
Affiliations:
Operations Research Center and Sloan School of Management Massachusetts Institute of Technology, , Cambridge MA 02139;Operations Research Center and Sloan School of Management Massachusetts Institute of Technology, , Cambridge MA 02139
Venue:
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Year:
2008

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Abstract

In this paper, we propose a general framework for designing fully polynomial time approximation schemes for combinatorial optimization problems, in which more than one objective function are combined into one using any norm. The main idea is to exploit the approximate Pareto-optimal frontier for multi-criteria optimization problems. Using this approach, we obtain an FPTAS for a novel resource allocation problem, for the problem of scheduling jobs on unrelated parallel machines, and for the Santa Claus problem, when the number of agents/machines is fixed, for any norm, including the l茂戮驴-norm. Moreover, either FPTAS can be implemented in a manner so that the space requirements are polynomial in all input parameters. We also give approximation algorithms and hardness results for the resource allocation problem when the number of agents is not fixed.