324 research outputs found

    Fully dynamic recognition of proper circular-arc graphs

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    We present a fully dynamic algorithm for the recognition of proper circular-arc (PCA) graphs. The allowed operations on the graph involve the insertion and removal of vertices (together with its incident edges) or edges. Edge operations cost O(log n) time, where n is the number of vertices of the graph, while vertex operations cost O(log n + d) time, where d is the degree of the modified vertex. We also show incremental and decremental algorithms that work in O(1) time per inserted or removed edge. As part of our algorithm, fully dynamic connectivity and co-connectivity algorithms that work in O(log n) time per operation are obtained. Also, an O(\Delta) time algorithm for determining if a PCA representation corresponds to a co-bipartite graph is provided, where \Delta\ is the maximum among the degrees of the vertices. When the graph is co-bipartite, a co-bipartition of each of its co-components is obtained within the same amount of time.Comment: 60 pages, 15 figure

    Search for microscopic black holes in pp collisions at √s̅ = 7 TeV

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    Mechanical stability of the CMS strip tracker measured with a laser alignment system

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    Search for leptophobic Z ' bosons decaying into four-lepton final states in proton-proton collisions at root s=8 TeV

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    Search for R-parity violating supersymmetry with displaced vertices in proton-proton collisions at root s=8 TeV

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