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- Rémy Belmonte, Martin Vatshelle
- Theor. Comput. Sci.
- 2013

Boolean-width is a recently introduced graph width parameter. If a boolean decomposition of width w is given, several NP-complete problems, such as Maximum Weight Independent Set, k-Coloring and… (More)

- Binh-Minh Bui-Xuan, Jan Arne Telle, Martin Vatshelle
- IWPEC
- 2009

- Binh-Minh Bui-Xuan, Jan Arne Telle, Martin Vatshelle
- Theor. Comput. Sci.
- 2013

Given a graph G we provide dynamic programming algorithms for many locally checkable vertex subset and vertex partitioning problems. Their runtime is polynomial in the number of equivalence classes… (More)

- Martin Vatshelle
- 2012

The main focus of this thesis is on using the divide and conquer technique to efficiently solve graph problems that are in general intractable. We work in the field of parameterized algorithms, using… (More)

- Daniel Lokshtanov, Martin Vatshelle, Yngve Villanger
- SODA
- 2013

The Independent Set problem is NP-hard in general, however polynomial time algorithms exist for the problem on various specific graph classes. Over the last couple of decades there has been a long… (More)

Boolean-width is a recently introduced graph invariant. Similar to tree-width, it measures the structural complexity of graphs. Given any graph G and a decomposition of G of boolean-width k, we give… (More)

- Binh-Minh Bui-Xuan, Jan Arne Telle, Martin Vatshelle
- Discrete Applied Mathematics
- 2010

We introduceH -join decompositions of graphs, indexed by a fixed bipartite graphH . These decompositions are based on a graph operation that we c ll H -join, which adds edges between two given graphs… (More)

- Sang-il Oum, Sigve Hortemo Sæther, Martin Vatshelle
- Theor. Comput. Sci.
- 2014

Many NP-hard problems, such as Dominating Set, are FPT parameterized by clique-width. For graphs of clique-width k given with a kexpression, Dominating Set can be solved in 4knO(1) time. However, no… (More)

- Michel Boyer, Sanae Harti, +7 authors Martin Vatshelle
- 2011

We explore cops-and-robbers games in several directions, giving partial results in each and refuting two reasonable conjectures. We close with some open problems.

- Sigve Hortemo Sæther, Jan Arne Telle, Martin Vatshelle
- J. Artif. Intell. Res.
- 2015

We look at dynamic programming algorithms for propositional model counting, also called #SAT, and MaxSAT. Tools from graph structure theory, in particular treewidth, have been used to successfully… (More)