62 research outputs found

    An FPT Algorithm for Spanning Trees with Few Branch Vertices Parameterized by Modular-Width

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    The minimum branch vertices spanning tree problem consists in finding a spanning tree T of an input graph G having the minimum number of branch vertices, that is, vertices of degree at least three in T. This NP-hard problem has been widely studied in the literature and has many important applications in network design and optimization. Algorithmic and combinatorial aspects of the problem have been extensively studied and its fixed parameter tractability has been recently considered. In this paper we focus on modular-width and show that the problem of finding a spanning tree with the minimum number of branch vertices is FPT with respect to this parameter

    Speeding up Networks Mining via Neighborhood Diversity

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    Parameterized complexity was classically used to efficiently solve NP-hard problems for small values of a fixed parameter. Then it has also been used as a tool to speed up algorithms for tractable problems. Following this line of research, we design algorithms parameterized by neighborhood diversity (nd) for several graph theoretic problems in P (e.g., Maximum Matching, Triangle counting and listing, Girth and Global minimum vertex cut). Such problems are known to admit algorithms parameterized by modular-width (mw) and consequently - being the nd a "special case" of mw - by nd. However, the proposed novel algorithms allow to improve the computational complexity from a time O(f(mw)? n +m) - where n and m denote, respectively, the number of vertices and edges in the input graph - which is multiplicative in n to a time O(g(nd)+n +m) which is additive only in the size of the input

    Measurements of the Higgs boson production and decay rates and coupling strengths using pp collision data at √S=7 and 8 TeV in the ATLAS experiment

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    Combined analyses of the Higgs boson production and decay rates as well as its coupling strengths to vector bosons and fermions are presented. The combinations include the results of the analyses of the H -> gamma gamma, ZZ*, WW*, Z gamma, b (b) over bar, tau tau and mu mu decay modes, and the constraints on the associated production with a pair of top quarks and on the off-shell coupling strengths of the Higgs boson. The results are based on the LHC proton-proton collision datasets, with integrated luminosities of up to 4.7 fb(-1) at root s = 7 TeV and 20.3 fb(-1) at root s = 8 TeV, recorded by the ATLAS detector in 2011 and 2012. Combining all production modes and decay channels, the measured signal yield, normalised to the Standard Model expectation, is 1.18(-0.14)(+0.15). The observed Higgs boson production and decay rates are interpreted in a leading-order coupling framework, exploring a wide range of benchmark coupling models both with and without assumptions on the Higgs boson width and on the Standard Model particle content in loop processes. The data are found to be compatible with the Standard Model expectations for a Higgs boson at a mass of 125.36 GeV for all models considered

    Search for single production of vector-like quarks decaying into Wb in pp collisions at s=8\sqrt{s} = 8 TeV with the ATLAS detector

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    Measurement of the charge asymmetry in top-quark pair production in the lepton-plus-jets final state in pp collision data at s=8TeV\sqrt{s}=8\,\mathrm TeV{} with the ATLAS detector

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    Measurement of the bbb\overline{b} dijet cross section in pp collisions at s=7\sqrt{s} = 7 TeV with the ATLAS detector

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    Charged-particle distributions at low transverse momentum in s=13\sqrt{s} = 13 TeV pppp interactions measured with the ATLAS detector at the LHC

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