Empirical Evaluation of Approximation Algorithms for Generalized Graph Coloring and Uniform Quasi-wideness

Nadara, Wojciech; Pilipczuk, Marcin; Rabinovich, Roman; Reidl, Felix; Siebertz, Sebastian

doi:10.1145/3368630

Cited by 14 publications

(25 citation statements)

References 69 publications

(112 reference statements)

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“…Being able to do this in linear time also ensures that indexing and querying can scale to very large data sets. Furthermore, because we utilize a broad structural characterization (bounded expansion) of cDBGs rather than a highly specialized aspect, our methods enable neighborhood-based information retrieval in any domain whose graphs exhibit bounded expansion structure; examples include some infrastructure, social, and communication networks [24,40,41].…”

Section: Efficient Graph Algorithms Provide Novel Tools For Investigamentioning

confidence: 99%

Exploring neighborhoods in large metagenome assembly graphs using spacegraphcats reveals hidden sequence diversity

et al. 2020

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Genomes computationally inferred from large metagenomic data sets are often incomplete and may be missing functionally important content and strain variation. We introduce an information retrieval system for large metagenomic data sets that exploits the sparsity of DNA assembly graphs to efficiently extract subgraphs surrounding an inferred genome. We apply this system to recover missing content from genome bins and show that substantial genomic sequence variation is present in a real metagenome. Our software implementation is available at https://github.com/ spacegraphcats/spacegraphcats under the 3-Clause BSD License.

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Section: Efficient Graph Algorithms Provide Novel Tools For Investigamentioning

confidence: 99%

Exploring neighborhoods in large metagenome assembly graphs using spacegraphcats reveals hidden sequence diversity

et al. 2020

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“…A purely combinatorial and effective proof has recently been given in [27]. Lower bounds, showing that polynomial bounds are the best one can hope for even on classes of graphs which exclude a fixed minor, were established in [21].…”

Section: Conclusion and Recent Resultsmentioning

confidence: 99%

Polynomial Kernels and Wideness Properties of Nowhere Dense Graph Classes

Kreutzer

Rabinovich

Siebertz

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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Nowhere dense classes of graphs [21,22] are very general classes of uniformly sparse graphs with several seemingly unrelated characterisations. From an algorithmic perspective, a characterisation of these classes in terms of uniform quasi-wideness, a concept originating in finite model theory, has proved to be particularly useful. Uniform quasi-wideness is used in many fpt-algorithms on nowhere dense classes. However, the existing constructions showing the equivalence of nowhere denseness and uniform quasi-wideness imply a non-elementary blow up in the parameter dependence of the fpt-algorithms, making them infeasible in practice.As a first main result of this paper, we use tools from logic, in particular from a sub-field of model theory known as stability theory, to establish polynomial bounds for the equivalence of nowhere denseness and uniform quasi-wideness.As an algorithmic application of our new methods, we obtain for every fixed value of r ∈ N a polynomial kernel for the distance-r dominating set problem on nowhere dense classes of graphs. This is particularly interesting, as it implies that for every subgraph-closed class C, the distance-r dominating set problem admits a kernel on C for every value of r if, and only if, it admits a polynomial kernel for every value of r (under the standard assumption of parameterized complexity theory that FPT ≠ W[2]).Finally, we demonstrate how to use the new methods to improve the parameter dependence of many fixedparameter algorithms. As an example we provide a single exponential parameterized algorithm for the Connected Dominating Set problem on nowhere dense graph

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Section: Discussionmentioning

confidence: 99%

Exploring neighborhoods in large metagenome assembly graphs reveals hidden sequence diversity

Brown¹,

Moritz

O’Brien

et al. 2018

Preprint

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Genomes computationally inferred from large metagenomic data sets are often incomplete and may be missing functionally important content and strain variation. We introduce an information retrieval system for large metagenomic data sets that exploits the sparsity of DNA assembly graphs to efficiently extract subgraphs surrounding an inferred genome. We apply this system to recover missing content from genome bins and show that substantial genomic sequence variation is present in a real metagenome. Our software implementation is available at https://github.com/spacegraphcats/ spacegraphcats under the 3-Clause BSD License. metagenomics | sequence assembly | strain variation | bounded expansion | dominating set * an invertible function that defines both an index and the corresponding inverted index

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Empirical Evaluation of Approximation Algorithms for Generalized Graph Coloring and Uniform Quasi-wideness

Cited by 14 publications

References 69 publications

Exploring neighborhoods in large metagenome assembly graphs using spacegraphcats reveals hidden sequence diversity

Exploring neighborhoods in large metagenome assembly graphs using spacegraphcats reveals hidden sequence diversity

Polynomial Kernels and Wideness Properties of Nowhere Dense Graph Classes

Exploring neighborhoods in large metagenome assembly graphs reveals hidden sequence diversity

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