Polynomial-Time Preprocessing for Weighted Problems Beyond Additive Goal Functions

10/01/2019
by   Matthias Bentert, et al.
0

Kernelization is the fundamental notion for polynomial-time prepocessing with performance guarantees in parameterized algorithmics. When preprocessing weighted problems, the need of shrinking weights might arise. Marx and Végh [ACM Trans. Algorithms 2015] and Etscheid et al. [J. Comput. Syst. Sci. 2017] used a technique due to Frank and Tardos [Combinatorica 1987] that we refer to as losing-weight technique to obtain kernels of polynomial size for weighted problems. While the mentioned earlier works focus on problems with additive goal functions, we focus on a broader class of goal functions. We lift the losing-weight technique to what we call linearizable goal functions, which also contain non-additive functions. We apply the lifted technique to five exemplary problems, thereby improving two results from the literature by proving polynomial kernels.

READ FULL TEXT

page 1

page 2

page 3

page 4

03/17/2021

On additive spanners in weighted graphs with local error

An additive +β spanner of a graph G is a subgraph which preserves distan...
04/29/2011

Limits of Preprocessing

We present a first theoretical analysis of the power of polynomial-time ...
04/24/2018

Polynomial Kernels for Hitting Forbidden Minors under Structural Parameterizations

We investigate polynomial-time preprocessing for the problem of hitting ...
05/08/2019

On the Approximate Compressibility of Connected Vertex Cover

The Connected Vertex Cover problem, where the goal is to compute a minim...
08/02/2018

A Class of Weighted TSPs with Applications

Motivated by applications to poaching and burglary prevention, we define...
07/06/2021

On the Hardness of Compressing Weights

We investigate computational problems involving large weights through th...
06/12/2014

Guarantees and Limits of Preprocessing in Constraint Satisfaction and Reasoning

We present a first theoretical analysis of the power of polynomial-time ...