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Science of Hitting
TitreScience of Hitting
Lancé4 years 10 days ago
Durée48 min 53 seconds
Nom de fichierscience-of-hitting_rNg5r.epub
science-of-hitting_ww25i.aac
Nombre de pages235 Pages
Taille1,343 KB
QualitéVorbis 96 kHz

Science of Hitting

Catégorie: Loisirs créatifs, décoration et passions, Sciences humaines, Famille et bien-être
Auteur: Kaylea Cross
Éditeur: John Cleese, Suzanne Fisher Staples
Publié: 2017-06-02
Écrivain: Adam Rubin
Langue: Vietnamien, Turc, Albanais, Japonais
Format: pdf, Livre audio
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Hitting minors, subdivisions, and immersions in tournaments - The Erd\Hos-P\'osa property relates parameters of covering and packing of combinatorial structures and has been mostly studied in the setting of undirected graphs. In this note, we use results of Chudnovsky, Fradkin, Kim, and Seymour to show that, for every directed graph $H$ (resp. strongly-connected directed graph $H$), the class of directed graphs that contain $H$ as a strong minor (resp. butterfly minor, topological minor) has the vertex-Erd\Hos-P\'osa property in the class of tournaments. We also prove that if $H$ is a strongly-connected directed graph, the class of directed graphs containing $H$ as an immersion has the edge-Erd\Hos-P\'osa property in the class of tournaments.
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Hitting minors on bounded treewidth graphs. II. Single-exponential algorithms - For a finite collection of graphs F, the F-M-Deletion (resp. F-TM-Deletion) problem consists in, given a graph G and an integer k, decide whether there exists S ⊆ V (G) with |S| ≤ k such that G \ S does not contain any of the graphs in F as a minor (resp. topological minor). We are interested in the parameterized complexity of both problems when the parameter is the treewidth of G, denoted by tw, and specifically in the cases where F contains a single connected planar graph H. We present algorithms running in time 2 O(tw) · n O(1) , called single-exponential, when H is either P 3 , P 4 , C 4 , the paw, the chair, and the banner for both H-M-Deletion and H-TM-Deletion, and when H = K 1,i , with i ≥ 1, for H-TM-Deletion. Some of these algorithms use the rank-based approach introduced by Bodlaender et al. [Inform Comput, 2015]. This is the second of a series of articles on this topic, and the results given here together with other ones allow us, in particular, to provide a tight dichotomy on the com
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Hitting Times in Markov Chains with Restart and their Application to Network Centrality - Motivated by applications in telecommunications, computer science and physics, we consider a discrete-time Markov process with restart. At each step the process either with a positive probability restarts from a given distribution, or with the complementary probability continues according to a Markov transition kernel. The main contribution of the present work is that we obtain an explicit expression for the expectation of the hitting time (to a given target set) of the process with restart. The formula is convenient when considering the problem of optimization of the expected hitting time with respect to the restart probability. We illustrate our results with two examples in uncountable and countable state spaces and with an application to network centrality.
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