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.H. Papadimitriou, M. Yannakakis, "On the approximability of trade-offs and optimal access of Web sources", FOCS, 2000, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 2000, pp. 86, doi:10.1109/SFCS.2000.892068