Outputs (58)

Complexity Framework for Forbidden Subgraphs I: The Framework (2025)
Journal Article
Johnson, M., Martin, B., Oostveen, J. J., Pandey, S., Paulusma, D., Smith, S., & van Leeuwen, E. J. (2025). Complexity Framework for Forbidden Subgraphs I: The Framework. Algorithmica, 87(3), 429-464. https://doi.org/10.1007/s00453-024-01289-2

For a set of graphs H, a graph G is H-subgraph-free if G does not contain any graph from H as a subgraph. We propose general and easy-to-state conditions on graph problems that explain a large set of results for H-subgraph-free graphs. Namely, a grap... Read More about Complexity Framework for Forbidden Subgraphs I: The Framework.

Complexity framework for forbidden subgraphs II: Edge subdivision and the "H"-graphs (2024)
Presentation / Conference Contribution
Lozin, V. V., Martin, B., Pandey, S., Paulusma, D., Siggers, M., Smith, S., & van Leeuwen, E. J. (2024, December). Complexity framework for forbidden subgraphs II: Edge subdivision and the "H"-graphs. Presented at ISAAC, ISAAC 2024

For a fixed set H of graphs, a graph G is H-subgraph-free if G does not contain any H ∈ H as a (not necessarily induced) subgraph. A recent framework gives a complete classification on H-subgraph-free graphs (for finite sets H) for problems that are... Read More about Complexity framework for forbidden subgraphs II: Edge subdivision and the "H"-graphs.

The Riis Complexity Gap for QBF Resolution (2024)
Journal Article
Beyersdorff, O., Clymo, J., Dantchev, S., & Martin, B. (2024). The Riis Complexity Gap for QBF Resolution. Journal on Satisfiability, Boolean Modeling and Computation, 15(1), 9-25. https://doi.org/10.3233/sat-231505

We give an analogue of the Riis Complexity Gap Theorem in Resolution for Quantified Boolean Formulas (QBFs). Every first-order sentence ϕ without finite models gives rise to a sequence of QBFs whose minimal refutations in tree-like QBF Resolution sys... Read More about The Riis Complexity Gap for QBF Resolution.

Complexity Classification Transfer for CSPs via Algebraic Products (2024)
Journal Article
Bodirsky, M., Jonsson, P., Martin, B., Mottet, A., & Semanišinová, Ž. (2024). Complexity Classification Transfer for CSPs via Algebraic Products. SIAM Journal on Computing, 53(5), 1293-1353. https://doi.org/10.1137/22m1534304

Proof Complexity and the Binary Encoding of Combinatorial Principles (2024)
Journal Article
Dantchev, S., Galesi, N., Ghani, A., & Martin, B. (2024). Proof Complexity and the Binary Encoding of Combinatorial Principles. SIAM Journal on Computing, 53(3), 764-802. https://doi.org/10.1137/20m134784x

Complexity framework for forbidden subgraphs IV: The Steiner Forest problem (2024)
Presentation / Conference Contribution
Bodlaender, H. L., Johnson, M., Martin, B., Oostveen, J. .., Pandey, S., Paulusma, D., Smith, S., & van Leeuwen, E. J. (2024, July). Complexity framework for forbidden subgraphs IV: The Steiner Forest problem. Presented at IWOCA, Ischia, Italy

Edge Multiway Cut and Node Multiway Cut are hard for planar subcubic graphs (2024)
Presentation / Conference Contribution
Johnson, M., Martin, B., Pandey, S., Paulusma, D., Smith, S., & van Leeuwen, E. J. (2024, June). Edge Multiway Cut and Node Multiway Cut are hard for planar subcubic graphs. Presented at SWAT 2024, Helsinki, Finland

It is known that the weighted version of Edge Multiway Cut (also known as Multiterminal Cut) is NP-complete on planar graphs of maximum degree 3. In contrast, for the unweighted version, NP-completeness is only known for planar graphs of maximum degr... Read More about Edge Multiway Cut and Node Multiway Cut are hard for planar subcubic graphs.

Depth lower bounds in Stabbing Planes for combinatorial principles (2024)
Journal Article
Dantchev, S., Galesi, N., Ghani, A., & Martin, B. (2024). Depth lower bounds in Stabbing Planes for combinatorial principles. Logical Methods in Computer Science, 20(1), 1-19. https://doi.org/10.46298/lmcs-20%281%3A1%292024

Stabbing Planes (also known as Branch and Cut) is a proof system introduced very recently which, informally speaking, extends the DPLL method by branching on integer linear inequalities instead of single variables. The techniques known so far to prov... Read More about Depth lower bounds in Stabbing Planes for combinatorial principles.

Complexity Framework for Forbidden Subgraphs III: When Problems are Tractable on Subcubic Graphs (2023)
Presentation / Conference Contribution
Johnson, M., Martin, B., Pandey, S., Paulusma, D., Smith, S., & Van Leeuwen, E. J. (2023, August). Complexity Framework for Forbidden Subgraphs III: When Problems are Tractable on Subcubic Graphs. Presented at 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023), Bordeaux, France

For any finite set H = {H1,. .. , Hp} of graphs, a graph is H-subgraph-free if it does not contain any of H1,. .. , Hp as a subgraph. In recent work, meta-classifications have been studied: these show that if graph problems satisfy certain prescribed... Read More about Complexity Framework for Forbidden Subgraphs III: When Problems are Tractable on Subcubic Graphs.

The Complexity of L(p, q)-Edge-Labelling (2023)
Journal Article
Berthe, G., Martin, B., Paulusma, D., & Smith, S. (2023). The Complexity of L(p, q)-Edge-Labelling. Algorithmica, 85(11), 3406-3429. https://doi.org/10.1007/s00453-023-01120-4

The L(p, q)-EDGE-LABELLING problem is the edge variant of the well-known L(p, q)-LABELLING problem. It is equivalent to the L(p, q)-LABELLING problem itself if we restrict the input of the latter problem to line graphs. So far, the complexity of L(p,... Read More about The Complexity of L(p, q)-Edge-Labelling.