English

Polynomial-Time Approximation Schemes for Independent Packing Problems on Fractionally Tree-Independence-Number-Fragile Graphs

Data Structures and Algorithms 2025-04-23 v1 Computational Geometry Combinatorics

Abstract

We investigate a relaxation of the notion of treewidth-fragility, namely tree-independence-number-fragility. In particular, we obtain polynomial-time approximation schemes for independent packing problems on fractionally tree-independence-number-fragile graph classes. Our approach unifies and extends several known polynomial-time approximation schemes on seemingly unrelated graph classes, such as classes of intersection graphs of fat objects in a fixed dimension or proper minor-closed classes. We also study the related notion of layered tree-independence number, a relaxation of layered treewidth.

Keywords

Cite

@article{arxiv.2303.07444,
  title  = {Polynomial-Time Approximation Schemes for Independent Packing Problems on Fractionally Tree-Independence-Number-Fragile Graphs},
  author = {Esther Galby and Andrea Munaro and Shizhou Yang},
  journal= {arXiv preprint arXiv:2303.07444},
  year   = {2025}
}

Comments

Full version of a paper to appear in a shorter form in the 39th International Symposium on Computational Geometry (SoCG 2023)