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Separating layered treewidth and row treewidth [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 Layered treewidth and row treewidth are recently introduced graph parameters that have been key ingredients in the solution of several well-known open problems.
Prosenjit Bose +4 more
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Treewidth-based algorithms for the small parsimony problem on networks [PDF]
Algorithms for Molecular Biology, 2022 Background Phylogenetic reconstruction is one of the paramount challenges of contemporary bioinformatics. A subtask of existing tree reconstruction algorithms is modeled by the Small Parsimony problem: given a tree T and an assignment of character-states
Celine Scornavacca, Mathias Weller
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A note on domino treewidth [PDF]
Discrete Mathematics & Theoretical Computer Science, 1999 In [DO95], Ding and Oporowski proved that for every k, and d, there exists a constant c_k,d, such that every graph with treewidth at most k and maximum degree at most d has domino treewidth at most c_k,d.
Hans L. Bodlaender
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Tree diet: reducing the treewidth to unlock FPT algorithms in RNA bioinformatics [PDF]
Algorithms for Molecular Biology, 2022 Hard graph problems are ubiquitous in Bioinformatics, inspiring the design of specialized Fixed-Parameter Tractable algorithms, many of which rely on a combination of tree-decomposition and dynamic programming.
Bertrand Marchand +2 more
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Maximum-scoring path sets on pangenome graphs of constant treewidth [PDF]
Frontiers in BioinformaticsWe generalize a problem of finding maximum-scoring segment sets, previously studied by Csűrös (IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2004, 1, 139–150), from sequences to graphs.
Broňa Brejová +3 more
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Automated design of dynamic programming schemes for RNA folding with pseudoknots [PDF]
Algorithms for Molecular Biology, 2023 Although RNA secondary structure prediction is a textbook application of dynamic programming (DP) and routine task in RNA structure analysis, it remains challenging whenever pseudoknots come into play.
Bertrand Marchand +4 more
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Treewidth 2 in the Planar Graph Product Structure Theorem [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe prove that every planar graph is contained in $H_1\boxtimes H_2\boxtimes K_2$ for some graphs $H_1$ and $H_2$ both with treewidth 2. This resolves a question of Liu, Norin and Wood [arXiv:2410.20333]. We also show this result is best possible: for any
Marc Distel +4 more
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On the treewidths of graphs of bounded degree. [PDF]
PLoS ONE, 2015 In this paper, we develop a new technique to study the treewidth of graphs with bounded degree. We show that the treewidth of a graph G = (V, E) with maximum vertex degree d is at most [Formula: see text] for sufficiently large d, where C is a constant.
Yinglei Song, Menghong Yu
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Benchmarking treewidth as a practical component of tensor network simulations. [PDF]
PLoS ONE, 2018 Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms.
Eugene F Dumitrescu +5 more
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The treewidth of 2-section of hypergraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Let $H=(V,F)$ be a simple hypergraph without loops. $H$ is called linear if $|f\cap g|\le 1$ for any $f,g\in F$ with $f\not=g$. The $2$-section of $H$, denoted by $[H]_2$, is a graph with $V([H]_2)=V$ and for any $ u,v\in V([H]_2)$, $uv\in E([H]_2)$ if ...
Ke Liu, Mei Lu
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