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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
doaj +4 more sources
Nordhaus-Gaddum for Treewidth [PDF]
European Journal of Combinatorics, 33.4:488-490, 2012, 2011 We prove that for every graph $G$ with $n$ vertices, the treewidth of $G$ plus the treewidth of the complement of $G$ is at least $n-2$. This bound is tight.
Bodlaender +12 more
arxiv +6 more sources
Degree-3 Treewidth Sparsifiers [PDF]
arXiv, 2014 We study treewidth sparsifiers. Informally, given a graph $G$ of treewidth $k$, a treewidth sparsifier $H$ is a minor of $G$, whose treewidth is close to $k$, $|V(H)|$ is small, and the maximum vertex degree in $H$ is bounded. Treewidth sparsifiers of degree $3$ are of particular interest, as routing on node-disjoint paths, and computing minors seems ...
Chekuri, Chandra, Chuzhoy, Julia
arxiv +7 more sources
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
doaj +6 more sources
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
doaj +2 more sources
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
doaj +2 more sources
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
doaj +2 more sources
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
doaj +2 more sources
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
doaj +2 more sources
Improved product structure for graphs on surfaces [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 Dujmovi\'c, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every graph $G$ with Euler genus $g$ there is a graph $H$ with treewidth at most 4 and a path $P$ such that $G\subseteq H \boxtimes P \boxtimes K_{\max\{2g,3\}}$. We improve
Marc Distel +3 more
doaj +1 more source