Data Reductions and Combinatorial Bounds for Improved Approximation Algorithms

TL;DR

This paper introduces a novel approach combining reduction rules and combinatorial insights to develop improved polynomial-time approximation algorithms for network security and information propagation problems.

Contribution

It presents a new method using approximation-preserving reductions inspired by parameterized complexity to enhance approximation algorithms.

Findings

Achieved the best approximation algorithms for Harmless Set, Differential, and Multiple Nonblocker.

Demonstrated the effectiveness of approximation-preserving reductions in algorithm design.

Applicable to problems related to network security and information dissemination.

Abstract

Kernelization algorithms in the context of Parameterized Complexity are often based on a combination of reduction rules and combinatorial insights. We will expose in this paper a similar strategy for obtaining polynomial-time approximation algorithms. Our method features the use of approximation-preserving reductions, akin to the notion of parameterized reductions. We exemplify this method to obtain the currently best approximation algorithms for \textsc{Harmless Set}, \textsc{Differential} and \textsc{Multiple Nonblocker}, all of them can be considered in the context of securing networks or information propagation.