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Reoptimization of parameterized problems.

Hans-Joachim Böckenhauer¹, Elisabet Burjons², Martin Raszyk¹

¹Department of Computer Science, ETH Zurich, Universitätsstrasse 6, Zurich, 8092 Switzerland.

Acta Informatica

|September 1, 2022

Summary

This summary is machine-generated.

This study explores parameterized complexity and reoptimization, revealing that some problems gain polynomial kernels under reoptimization, while others remain complex. This advances understanding of computational problem classification.

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Area of Science:

Theoretical Computer Science
Computational Complexity Theory

Background:

Parameterized complexity analyzes algorithms based on a parameter.
Reoptimization seeks solutions for modified problem instances.
Combining these offers new insights into problem complexity.

Purpose of the Study:

To investigate the interplay between parameterized complexity and reoptimization.
To classify the complexity of compositional problems under reoptimization.
To identify conditions under which polynomial kernels emerge or are refuted.

Main Methods:

Analysis of compositional problems within the parameterized reoptimization framework.
Exploration of local modifications and their impact on kernelization.
Application of techniques like crown decompositions for specific problems.

Main Results:

Some compositional problems gain polynomial kernels under specific reoptimization local modifications.
Other local modifications do not yield polynomial kernels, even under standard assumptions.
The reoptimization of Connected Vertex Cover lacks a polynomial kernel unless Set Cover has a polynomial compression.
The reoptimization of Vertex Cover achieves a smaller polynomial kernel using crown decompositions.

Conclusions:

Reoptimization can alter the parameterized complexity landscape of problems.
The existence of polynomial kernels is sensitive to the type of modification in reoptimization.
This research refines the understanding of kernelization for parameterized problems.