Polynomial Kernels for Weighted Problems

Michael Etscheid, Stefan Kratsch, Matthias Mnich, Heiko Röglin

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


Kernelization is a formalization of efficient preprocessing for \mathsf {np}\mathsf {np}-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial kernelizations for subset sum and knapsack when parameterized by the number n of items.we answer both questions affirmatively by using an algorithm for compressing numbers due to frank and tardos (combinatorica 1987). This result had been first used by marx and végh (icalp 2013) in the context of kernelization. We further illustrate its applicability by giving polynomial kernels also for weighted versions of several well-studied parameterized problems. Furthermore, when parameterized by the different item sizes we obtain a polynomial kernelization for subset sum and an exponential kernelization for knapsack. Finally, we also obtain kernelization results for polynomial integer programs.
Original languageEnglish
Title of host publicationMathematical Foundations of Computer Science 2015
Subtitle of host publication40th International Symposium, MFCS 2015 Milan, Italy, August 24-28, 2015, Proceedings Part II
EditorsGiuseppe F. Italiano, Giovanni Pighizzini, Donald T. Sannella
ISBN (Electronic)978-3-662-48054-0
ISBN (Print)978-3-662-48053-3
Publication statusPublished - 2015
Externally publishedYes

Publication series

SeriesLecture Notes in Computer Science

Cite this

Etscheid, M., Kratsch, S., Mnich, M., & Röglin, H. (2015). Polynomial Kernels for Weighted Problems. In G. F. Italiano, G. Pighizzini, & D. T. Sannella (Eds.), Mathematical Foundations of Computer Science 2015: 40th International Symposium, MFCS 2015 Milan, Italy, August 24-28, 2015, Proceedings Part II (pp. 287-298). Springer. Lecture Notes in Computer Science, Vol.. 9235 https://doi.org/10.1007/978-3-662-48054-0_24