Parameterized Algorithmics for Graph Modification Problems: On Interactions with Heuristics

TL;DR

This paper explores the relationship between fixed-parameter algorithms and heuristics in solving NP-hard graph modification problems, highlighting how these approaches can inform and improve each other.

Contribution

It provides a detailed analysis of the interactions between parameterized algorithms and heuristics, demonstrating mutual benefits in tackling graph modification problems.

Findings

Fixed-parameter algorithms can guide heuristic development.

Heuristics can inform the design of fixed-parameter algorithms.

Combined approaches improve practical solutions for NP-hard problems.

Abstract

In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster Deletion problem asks to delete as few edges as possible such that the resulting graph is a disjoint union of cliques. Graph modification problems appear in numerous applications, including the analysis of biological and social networks. Typically, graph modification problems are NP-hard, making them natural candidates for parameterized complexity studies. We discuss several fruitful interactions between the development of fixed-parameter algorithms and the design of heuristics for graph modification problems, featuring quite different aspects of mutual benefits.