ToTo: An open database for computation, storage and retrieval of tree decompositions

Wersch, Rim van; Kelk, Steven

doi:10.1016/j.dam.2016.09.023

Cited by 4 publications

(4 citation statements)

References 8 publications

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“…Our analysis ignores nodes that offer under 50% accuracy and nodes that contain very few (less than four) samples, as those are deemed not to bring a significant amount of insight to the analysis. q1 ≤ 4.5 gini = 0.594 samples = 213 salue= [24,93,96] class = tdlib entropy ≤ 4.73 gini = 0.452 samples = 116 salue= [11,23,82] class = tdlib minimum ≤ 3.5 gini = 0.321 samples = 90 salue= [5,12,73] class= tdlib gini = 0.281 samples = 87 salue= [4,10,73] class = tdlib variation ≤ 0.603 gini = 0.44 samples = 97 salue= [13,70,14] class The first line in each internal node indicates the condition according to which that node splits instances.…”

Section: Discussionmentioning

confidence: 99%

“…This does not nullify its usefulness, however. Alongside practical heuristics (see e.g., References [9,10]) there is an extensive literature on computing the treewidth of a graph exactly, in spite of its NP-hardness. Some of these results have a purely theoretical flavour, most famously in Reference [11] but there has also been a consistent stream of research on computing treewidth exactly in practice.…”

Section: The Importance Of Treewidthmentioning

confidence: 99%

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A Machine Learning Approach to Algorithm Selection for Exact Computation of Treewidth

2019

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We present an algorithm selection framework based on machine learning for the exact computation of treewidth, an intensively studied graph parameter that is NP-hard to compute. Specifically, we analyse the comparative performance of three state-of-the-art exact treewidth algorithms on a wide array of graphs and use this information to predict which of the algorithms, on a graph by graph basis, will compute the treewidth the quickest. Experimental results show that the proposed meta-algorithm outperforms existing methods on benchmark instances on all three performance metrics we use: in a nutshell, it computes treewidth faster than any single algorithm in isolation. We analyse our results to derive insights about graph feature importance and the strengths and weaknesses of the algorithms we used. Our results are further evidence of the advantages to be gained by strategically blending machine learning and combinatorial optimisation approaches within a hybrid algorithmic framework. The machine learning model we use is intentionally simple to emphasise that speedup can already be obtained without having to engage in the full complexities of machine learning engineering. We reflect on how future work could extend this simple but effective, proof-of-concept by deploying more sophisticated machine learning models.

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Section: Discussionmentioning

confidence: 99%

Section: The Importance Of Treewidthmentioning

confidence: 99%

A Machine Learning Approach to Algorithm Selection for Exact Computation of Treewidth

2019

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“…Their adjacency matrices are listed in Figure 2 in the same order. The adjacency matrices were obtained from the database [82] with the help of the online converter [114]. The top-left graph in Figure 1 is an example of a Paley graph Paley(q), which has a finite field F q as its vertex set, where q = 1 (mod 4), and two elements in F q form an edge if any only if their difference is a nonzero square element in F q .…”

Section: Self-complementary Graphsmentioning

confidence: 99%

A family of non-Cayley cores based on vertex-transitive or strongly regular self-complementary graphs

Orel¹

2021

Preprint

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Given a finite simple graph Γ on n vertices its complementary prism is the graph Γ Γ that is obtained from Γ and its complement Γ by adding a perfect matching, where each its edge connects two copies of the same vertex in Γ and Γ. It generalizes the Petersen graph, which is obtained if Γ is the pentagon. The automorphism group of Γ Γ is described for arbitrary graph Γ. In particular, it is shown that the ratio between the cardinalities of the automorphism groups of Γ Γ and Γ can attain only values 1, 2, 4, and 12. It is shown that the Cheeger number of Γ Γ equals either 1 or 1 − 1 n , and the two corresponding classes of graphs are fully determined. It is proved that Γ Γ is vertex-transitive if and only if Γ is vertex-transitive and self-complementary. In this case the complementary prism is Hamiltonian-connected whenever n > 5, and is not a Cayley graph whenever n > 1. The main results involve endomorphisms of graph Γ Γ. It is shown that Γ Γ is a core, i.e. all its endomorphisms are automorphisms, whenever Γ is strongly regular and self-complementary. The same conclusion is obtained for many vertex-transitive self-complementary graphs. In particular, it is shown that if there exists a vertex-transitive self-complementary graph Γ such that Γ Γ is not a core, then Γ is neither a core nor its core is a complete graph.

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“…The reader may check the central case sig(G) = AAL AAL AAL either by hand or, e.g., using ToTo[50]. The other cases follow since they are minors of this G.…”

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confidence: 99%

Characterizing 2-crossing-critical graphs

Bokal

Oporowski

Richter

et al. 2016

Advances in Applied Mathematics

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A c-crossing-critical graph is one that has crossing number at least c but each of its proper subgraphs has crossing number less than c. Recently, a set of explicit construction rules was identified by Bokal, Oporowski, Richter, and Salazar to generate all large 2-crossing-critical graphs (i.e., all apart from a finite set of small sporadic graphs). They share the property of containing a generalized Wagner graph V10 as a subdivision.In this paper, we study these graphs and establish their order, simple crossing number, edge cover number, clique number, maximum degree, chromatic number, chromatic index, and treewidth. We also show that the graphs are linear-time recognizable and that all our proofs lead to efficient algorithms for the above measures.

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ToTo: An open database for computation, storage and retrieval of tree decompositions

Cited by 4 publications

References 8 publications

A Machine Learning Approach to Algorithm Selection for Exact Computation of Treewidth

A Machine Learning Approach to Algorithm Selection for Exact Computation of Treewidth

A family of non-Cayley cores based on vertex-transitive or strongly regular self-complementary graphs

Characterizing 2-crossing-critical graphs

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