Kernelization Lower Bounds for Finding Constant-Size Subgraphs

Fluschnik, T.; Mertzios, G.B.; Nichterlein, A.

Abstract

Kernelization is an important tool in parameterized algorithmics. Given an input instance accompanied by a parameter, the goal is to compute in polynomial time an equivalent instance of the same problem such that the size of the reduced instance only depends on the parameter and not on the size of the original instance. In this paper, we provide a first conceptual study on limits of kernelization for several polynomial-time solvable problems. For instance, we consider the problem of finding a triangle with negative sum of edge weights parameterized by the maximum degree of the input graph. We prove that a linear-time computable strict kernel of truly subcubic size for this problem violates the popular APSP-conjecture.

Citation

Fluschnik, T., Mertzios, G., & Nichterlein, A. (2018). Kernelization Lower Bounds for Finding Constant-Size Subgraphs. In F. Manea, R. Miller, & D. Nowotka (Eds.), Sailing routes in the world of computation : 14th Conference on Computability in Europe, CiE 2018, Kiel, Germany, July 30-August 3, 2018. Proceedings (183-193). Springer Verlag. https://doi.org/10.1007/978-3-319-94418-0_19

• Online Publication Date: Jul 3, 2018
• Publication Date: Jul 3, 2018
• Deposit Date: Sep 12, 2018
• Publicly Available Date: Sep 13, 2018
• Publisher: Springer Verlag
• Pages: 183-193
• Series Title: Lecture notes in computer science
• Book Title: Sailing routes in the world of computation : 14th Conference on Computability in Europe, CiE 2018, Kiel, Germany, July 30-August 3, 2018. Proceedings.
• ISBN: 9783319944173
• DOI: https://doi.org/10.1007/978-3-319-94418-0_19
• Public URL: https://durham-repository.worktribe.com/output/1635008
• Contract Date: Apr 6, 2018