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Polynomial-Time Data Reduction for Weighted Problems Beyond Additive Goal Functions
arXiv - CS - Discrete Mathematics Pub Date : 2019-10-01 , DOI: arxiv-1910.00277
Matthias Bentert; René van Bevern; Till Fluschnik; André Nichterlein; Rolf Niedermeier

Kernelization is the fundamental notion for polynomial-time data reduction with performance guarantees. Kernelization for weighted problems particularly requires to also shrink weights. Marx and V\'egh [ACM Trans. Algorithms 2015] and Etscheid et al. [J. Comput. Syst. Sci. 2017] used a technique of Frank and Tardos [Combinatorica 1987] to obtain polynomial-size kernels for weighted problems, mostly with additive goal functions. We lift the technique to linearizable functions, a function type that we introduce and that also contains non-additive functions. Using the lifted technique, we obtain kernelization results for natural problems in graph partitioning, network design, facility location, scheduling, vehicle routing, and computational social choice, thereby improving and generalizing results from the literature.
更新日期:2020-02-19

 

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