Proceedings 41st Annual Symposium on Foundations of Computer Science (2000)
Redondo Beach, California
Nov. 12, 2000 to Nov. 14, 2000
C.H. Papadimitriou , Dept. of Comput. Sci., California Univ., Berkeley, CA, USA
M. Yannakakis , Dept. of Comput. Sci., California Univ., Berkeley, CA, USA
We study problems in multiobjective optimization, in which solutions to a combinatorial optimization problem are evaluated with respect to several cost criteria, and we are interested in the trade-off between these objectives (the so-called Pareto curve). We point out that, under very general conditions, there is a polynomially succinct curve that /spl epsiv/-approximates the Pareto curve, for any /spl epsiv/<0. We give a necessary and sufficient condition under which this approximate Pareto curve can be constructed in time polynomial in the size of the instance and 1//spl epsiv/. In the case of multiple linear objectives, we distinguish between two cases: when the underlying feasible region is convex, then we show that approximating the multi-objective problem is equivalent to approximating the single-objective problem. If however the feasible region is discrete, then we point out that the question reduces to an old and recurrent one: how does the complexity of a combinatorial optimization problem change when its feasible region is intersected with a hyperplane with small coefficients; we report some interesting new findings in this domain. Finally, we apply these concepts and techniques to formulate and solve approximately a cost-time-quality trade-off for optimizing access to the World-Wide Web, in a model first studied by Etzioni et al. (1996) (which was actually the original motivation for this work).
information resources; optimisation; combinatorial mathematics; computational complexity; information retrieval; Web sources; optimal access; trade-offs; approximability; multiobjective optimization; combinatorial optimization problem; cost criteria; Pareto curve; polynomially succinct curve; multiple linear objectives; complexity; hyperplane; cost-time-quality trade-off; World-Wide Web
C. Papadimitriou and M. Yannakakis, "On the approximability of trade-offs and optimal access of Web sources," Proceedings 41st Annual Symposium on Foundations of Computer Science(FOCS), Redondo Beach, California, 2000, pp. 86.