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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 and Ren\'e van Bevern and Till Fluschnik and Andr\'e Nichterlein and Rolf Niedermeier
arXiv - CS - Discrete Mathematics Pub Date : 2019-10-01 , DOI: arxiv-1910.00277 Matthias Bentert and Ren\'e van Bevern and Till Fluschnik and Andr\'e Nichterlein and 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