Incremental-Decremental Maximization

Annette Lutz ( TU Darmstadt )

Incremental–decremental maximization captures the gradual transformation or renewal of infrastructures. An initial solution is transformed one element at a time and the utility of an intermediate solution is given by the sum of the utilities of the transformed and untransformed parts. We propose a simple randomized and a deterministic algorithm that both find an order in which to transform the elements while maintaining a large utility during all stages of transformation, relative to an optimum solution for the current stage. More specifically, our algorithms yield competitive solutions for utility functions of bounded curvature and/or generic submodularity ratio, and, in particular, for submodular functions, and gross substitute functions. Our results exhibit that incremental–decremental maximization is substantially more difficult than incremental maximization.

This is joint work with Yann Disser, Max Klimm and Lea Strubberg.