Parameterized lower bound and NP-completeness of some HH-free Edge Deletion problems

For a graph $H$, the $H$-free Edge Deletion problem asks whether there exist at most $k$ edges whose deletion from the input graph $G$ results in a graph without any induced copy of $H$. We prove that $H$-free Edge Deletion is NP-complete if $H$ is a graph with at least two edges and $H$ has a component with maximum number of vertices which is a tree or a regular graph. Furthermore, we obtain that these NP-complete problems cannot be solved in parameterized subexponential time, i.e., in time $2^{o(k)}\cdot |G|^{O(1)}$, unless Exponential Time Hypothesis fails.Comment: 15 pages, COCOA 15 accepted pape

Parameterized vertex deletion problems for hereditary graph classes with a block property

For a class of graphs P, the Bounded P-Block Vertex Deletion problem asks, given a graph G on n vertices and positive integers k and d, whether there is a set S of at most k vertices such that each block of G − S has at most d vertices and is in P. We show that when P satisfies a natural hereditary property and is recognizable in polynomial time, Bounded P-Block Vertex Deletion can be solved in time 2O(k log d)nO(1), and this running time cannot be improved to 2o(k log d)nO(1), in general, unless the Exponential Time Hypothesis fails. On the other hand, if P consists of only complete graphs, or only K1,K2, and cycle graphs, then Bounded P-Block Vertex Deletion admits a cknO(1)-time algorithm for some constant c independent of d. We also show that Bounded P-Block Vertex Deletion admits a kernel with O(k2d7) vertices. © Springer-Verlag GmbH Germany 2016

Deleting edges to restrict the size of an epidemic: a new application for treewidth

Motivated by applications in network epidemiology, we consider the problem of determining whether it is possible to delete at most k edges from a given input graph (of small treewidth) so that the resulting graph avoids a set FF of forbidden subgraphs; of particular interest is the problem of determining whether it is possible to delete at most k edges so that the resulting graph has no connected component of more than h vertices, as this bounds the worst-case size of an epidemic. While even this special case of the problem is NP-complete in general (even when h=3h=3 ), we provide evidence that many of the real-world networks of interest are likely to have small treewidth, and we describe an algorithm which solves the general problem in time 2O(|F|wr)n2O(|F|wr)n  on an input graph having n vertices and whose treewidth is bounded by a fixed constant w, if each of the subgraphs we wish to avoid has at most r vertices. For the special case in which we wish only to ensure that no component has more than h vertices, we improve on this to give an algorithm running in time O((wh)2wn)O((wh)2wn) , which we have implemented and tested on real datasets based on cattle movements

ICAR: endoscopic skull‐base surgery

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Subgraph isomorphism on graph classes that exclude a substructure

\u3cp\u3eWe study Subgraph Isomorphism on graph classes defined by a fixed forbidden graph. Although there are several ways for forbidding a graph, we observe that it is reasonable to focus on the minor relation since other well-known relations lead to either trivial or equivalent problems. When the forbidden minor is connected, we present a near dichotomy of the complexity of Subgraph Isomorphism with respect to the forbidden minor, where the only unsettled case is the path of five vertices. We then also consider the general case of possibly disconnected forbidden minors. We show in particular that: the problem is fixed-parameter tractable parameterized by the size of the forbidden minor H when H is a linear forest such that at most one component has four vertices and all other components have three or less vertices; and it is NP-complete if H contains four or more components with at least five vertices each. As a byproduct, we show that Subgraph Isomorphism is fixed-parameter tractable parameterized by vertex integrity. Using similar techniques, we also observe that Subgraph Isomorphism is fixed-parameter tractable parameterized by neighborhood diversity.\u3c/p\u3

An assessment of Southern Ocean water masses and sea ice during 1988-2007 in a suite of interannual CORE-II simulations

We characterise the representation of the Southern Ocean water mass structure and sea ice within a suite of 15 global ocean-ice models run with the Coordinated Ocean-ice Reference Experiment Phase II (CORE-II) protocol. The main focus is the representation of the present (1988-2007) mode and intermediate waters, thus framing an analysis of winter and summer mixed layer depths; temperature, salinity, and potential vorticity structure; and temporal variability of sea ice distributions. We also consider the interannual variability over the same 20 year period. Comparisons are made between models as well as to observation-based analyses where available. The CORE-II models exhibit several biases relative to Southern Ocean observations, including an underestimation of the model mean mixed layer depths of mode and intermediate water masses in March (associated with greater ocean surface heat gain), and an overestimation in September (associated with greater high latitude ocean heat loss and a more northward winter sea-ice extent). In addition, the models have cold and fresh/warm and salty water column biases centred near 50 degrees S. Over the 1933-2007 period, the CORE-II models consistently simulate spatially variable trends in sea-ice concentration, surface freshwater fluxes, mixed layer depths, and 200-700 in ocean heat content. In particular, sea-ice coverage around most of the Antarctic continental shelf is reduced, leading to a cooling and freshening of the near surface waters. The shoaling of the mixed layer is associated with increased surface buoyancy gain, except in the Pacific where sea ice is also influential. The models are in disagreement, despite the common CORE-II atmospheric state, in their spatial pattern of the 20-year trends in the mixed layer depth and sea-ice. (C) 2015 Elsevier Ltd. All rights reserved