Twin-width III: max independent set, min dominating set, and coloring

É Bonnet, C Geniet, EJ Kim, S Thomassé… - SIAM Journal on …, 2024 - SIAM
We recently introduced the notion of twin-width, a novel graph invariant, and showed that
first-order model checking can be solved in time for-vertex graphs given with a witness that …

Independent Set on -Free Graphs in Quasi-Polynomial Time

P Gartland, D Lokshtanov - 2020 IEEE 61st Annual Symposium …, 2020 - ieeexplore.ieee.org
We present an algorithm that takes as input a graph G with weights on the vertices, and
computes a maximum weight independent set S of G. If the input graph G excludes a path P …

Quasi-polynomial-time algorithm for Independent Set in Pt-free graphs via shrinking the space of induced paths

M Pilipczuk, M Pilipczuk, P Rzążewski - Symposium on Simplicity in Algorithms …, 2021 - SIAM
In a recent breakthrough work, Gartland and Lokshtanov [FOCS 2020] showed a quasi-
polynomial-time algorithm for Maximum Weight Independent Set in Pt-free graphs, that is …

[HTML][HTML] Treewidth versus clique number. III. Tree-independence number of graphs with a forbidden structure

C Dallard, M Milanič, K Štorgel - Journal of Combinatorial Theory, Series B, 2024 - Elsevier
We continue the study of (tw, ω)-bounded graph classes, that is, hereditary graph classes in
which the treewidth can only be large due to the presence of a large clique, with the goal of …

Finding large induced sparse subgraphs in c>t -free graphs in quasipolynomial time

P Gartland, D Lokshtanov, M Pilipczuk… - Proceedings of the 53rd …, 2021 - dl.acm.org
For an integer t, a graph G is called C> t-free if G does not contain any induced cycle on
more than t vertices. We prove the following statement: for every pair of integers d and t and …

Maximum weight independent set in graphs with no long claws in quasi-polynomial time

P Gartland, D Lokshtanov, T Masařík… - Proceedings of the 56th …, 2024 - dl.acm.org
We show that the Maximum Weight Independent Set problem (MWIS) can be solved in quasi-
polynomial time on H-free graphs (graphs excluding a fixed graph H as an induced …

Induced subgraphs of bounded treewidth and the container method

T Abrishami, M Chudnovsky, M Pilipczuk… - SIAM Journal on …, 2024 - SIAM
A hole in a graph is an induced cycle of length at least 4. A hole is long if its length is at least
5. By, we denote a path on vertices. In this paper, we give polynomial-time algorithms for the …

Tree decompositions meet induced matchings: beyond Max Weight Independent Set

PT Lima, M Milanič, P Muršič, K Okrasa… - arXiv preprint arXiv …, 2024 - arxiv.org
For a tree decomposition $\mathcal {T} $ of a graph $ G $, by $\mu (\mathcal {T}) $ we
denote the size of a largest induced matching in $ G $ all of whose edges intersect one bag …

Polynomial-time algorithm for maximum independent set in bounded-degree graphs with no long induced claws

T Abrishami, M Chudnovsky, C Dibek… - Proceedings of the 2022 …, 2022 - SIAM
For graphs G and H, we say that G is H-free if it does not contain H as an induced subgraph.
Already in the early 1980s Alekseev observed that if H is connected, then the Max Weight …

Heavy-head sampling for fast imitation learning of machine learning based combinatorial auction solver

C Peng, B Liao - Neural Processing Letters, 2023 - Springer
The winner determination problem of a combinatorial auction can be modeled as mixed-
integer linear programming, and is a popular benchmark to evaluate modern solvers …