The Hardness of Embedding Grids and Walls

The dichotomy conjecture for the parameterized embedding problem states that the problem of deciding whether a given graph $G$ from some class $K$ of "pattern graphs" can be embedded into a given graph $H$ (that is, is isomorphic to a subgraph of $H$) is fixed-parameter tractable if $K$ is a class of graphs of bounded tree width and $W[1]$-complete otherwise. Towards this conjecture, we prove that the embedding problem is $W[1]$-complete if $K$ is the class of all grids or the class of all walls

Improved FPT algorithms for weighted independent set in bull-free graphs

Very recently, Thomass\'e, Trotignon and Vuskovic [WG 2014] have given an FPT algorithm for Weighted Independent Set in bull-free graphs parameterized by the weight of the solution, running in time $2^{O(k^5)} \cdot n^9$. In this article we improve this running time to $2^{O(k^2)} \cdot n^7$. As a byproduct, we also improve the previous Turing-kernel for this problem from $O(k^5)$ to $O(k^2)$. Furthermore, for the subclass of bull-free graphs without holes of length at most $2p-1$ for $p \geq 3$, we speed up the running time to $2^{O(k \cdot k^{\frac{1}{p-1}})} \cdot n^7$. As $p$ grows, this running time is asymptotically tight in terms of $k$, since we prove that for each integer $p \geq 3$, Weighted Independent Set cannot be solved in time $2^{o(k)} \cdot n^{O(1)}$ in the class of $\{bull,C_4,\ldots,C_{2p-1}\}$-free graphs unless the ETH fails.Comment: 15 page

On The Power of Tree Projections: Structural Tractability of Enumerating CSP Solutions

The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a computation problem where the focus is either on finding one solution, or on enumerating all solutions, possibly projected to some given set of output variables. The paper investigates the structural tractability of the problem of enumerating (possibly projected) solutions, where tractability means here computable with polynomial delay (WPD), since in general exponentially many solutions may be computed. A general framework based on the notion of tree projection of hypergraphs is considered, which generalizes all known decomposition methods. Tractability results have been obtained both for classes of structures where output variables are part of their specification, and for classes of structures where computability WPD must be ensured for any possible set of output variables. These results are shown to be tight, by exhibiting dichotomies for classes of structures having bounded arity and where the tree decomposition method is considered

Parametrised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic

In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parametrisations with respect to the central decision problems. The model checking problem (MC) of PDL is NP-complete. The subject of this research is to identify a list of parametrisations (formula-size, treewidth, treedepth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) showing a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is in FPT. Finally, we introduce a variant of the satisfiability problem, asking for teams of a given size, and show for this problem an almost complete picture.Comment: Update includes refined result

The Power of Cut-Based Parameters for Computing Edge Disjoint Paths

This paper revisits the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal pair in P. Our aim is to identify structural properties (parameters) of graphs which allow the efficient solution of EDP without restricting the placement of terminals in P in any way. In this setting, EDP is known to remain NP-hard even on extremely restricted graph classes, such as graphs with a vertex cover of size 3. We present three results which use edge-separator based parameters to chart new islands of tractability in the complexity landscape of EDP. Our first and main result utilizes the fairly recent structural parameter treecut width (a parameter with fundamental ties to graph immersions and graph cuts): we obtain a polynomial-time algorithm for EDP on every graph class of bounded treecut width. Our second result shows that EDP parameterized by treecut width is unlikely to be fixed-parameter tractable. Our final, third result is a polynomial kernel for EDP parameterized by the size of a minimum feedback edge set in the graph

The incidence and clinical burden of respiratory syncytial virus disease identified through hospital outpatient presentations in Kenyan children

There is little information that describe the burden of respiratory syncytial virus (RSV) associated disease in the tropical African outpatient setting. Methods We studied a systematic sample of children aged <5 years presenting to a rural district hospital in Kenya with acute respiratory infection (ARI) between May 2002 and April 2004. We collected clinical data and screened nasal wash samples for RSV antigen by immunofluorescence. We used a linked demographic surveillance system to estimate disease incidence. Results Among 2143 children tested, 166 (8%) were RSV positive (6% among children with upper respiratory tract infection and 12% among children with lower respiratory tract infection (LRTI). RSV was more likely in LRTI than URTI (p<0.001). 51% of RSV cases were aged 1 year or over. RSV cases represented 3.4% of hospital outpatient presentations. Relative to RSV negative cases, RSV positive cases were more likely to have crackles (RR = 1.63; 95% CI 1.34–1.97), nasal flaring (RR = 2.66; 95% CI 1.40–5.04), in-drawing (RR = 2.24; 95% CI 1.47–3.40), fast breathing for age (RR = 1.34; 95% CI 1.03–1.75) and fever (RR = 1.54; 95% CI 1.33–1.80). The estimated incidence of RSV-ARI and RSV-LRTI, per 100,000 child years, among those aged <5 years was 767 and 283, respectively. Conclusion The burden of childhood RSV-associated URTI and LRTI presenting to outpatients in this setting is considerable. The clinical features of cases associated with an RSV infection were more severe than cases without an RSV diagnosis

Performance of Small Cluster Surveys and the Clustered LQAS Design to estimate Local-level Vaccination Coverage in Mali

<p>Abstract</p> <p>Background</p> <p>Estimation of vaccination coverage at the local level is essential to identify communities that may require additional support. Cluster surveys can be used in resource-poor settings, when population figures are inaccurate. To be feasible, cluster samples need to be small, without losing robustness of results. The clustered LQAS (CLQAS) approach has been proposed as an alternative, as smaller sample sizes are required.</p> <p>Methods</p> <p>We explored (i) the efficiency of cluster surveys of decreasing sample size through bootstrapping analysis and (ii) the performance of CLQAS under three alternative sampling plans to classify local VC, using data from a survey carried out in Mali after mass vaccination against meningococcal meningitis group A.</p> <p>Results</p> <p>VC estimates provided by a 10 × 15 cluster survey design were reasonably robust. We used them to classify health areas in three categories and guide mop-up activities: i) health areas not requiring supplemental activities; ii) health areas requiring additional vaccination; iii) health areas requiring further evaluation. As sample size decreased (from 10 × 15 to 10 × 3), standard error of VC and ICC estimates were increasingly unstable. Results of CLQAS simulations were not accurate for most health areas, with an overall risk of misclassification greater than 0.25 in one health area out of three. It was greater than 0.50 in one health area out of two under two of the three sampling plans.</p> <p>Conclusions</p> <p>Small sample cluster surveys (10 × 15) are acceptably robust for classification of VC at local level. We do not recommend the CLQAS method as currently formulated for evaluating vaccination programmes.</p

Hamiltonian Cycle Parameterized by Treedepth in Single Exponential Time and Polynomial Space

For many algorithmic problems on graphs of treewidth $t$, a standard dynamic programming approach gives an algorithm with time and space complexity $2^{\mathcal{O}(t)}\cdot n^{\mathcal{O}(1)}$. It turns out that when one considers the more restrictive parameter treedepth, it is often the case that a variation of this technique can be used to reduce the space complexity to polynomial, while retaining time complexity of the form $2^{\mathcal{O}(d)}\cdot n^{\mathcal{O}(1)}$, where $d$ is the treedepth. This transfer of methodology is, however, far from automatic. For instance, for problems with connectivity constraints, standard dynamic programming techniques give algorithms with time and space complexity $2^{\mathcal{O}(t\log t)}\cdot n^{\mathcal{O}(1)}$ on graphs of treewidth $t$, but it is not clear how to convert them into time-efficient polynomial space algorithms for graphs of low treedepth. Cygan et al. (FOCS'11) introduced the Cut&Count technique and showed that a certain class of problems with connectivity constraints can be solved in time and space complexity $2^{\mathcal{O}(t)}\cdot n^{\mathcal{O}(1)}$. Recently, Hegerfeld and Kratsch (STACS'20) showed that, for some of those problems, the Cut&Count technique can be also applied in the setting of treedepth, and it gives algorithms with running time $2^{\mathcal{O}(d)}\cdot n^{\mathcal{O}(1)}$ and polynomial space usage. However, a number of important problems eluded such a treatment, with the most prominent examples being Hamiltonian Cycle and Longest Path. In this paper we clarify the situation by showing that Hamiltonian Cycle, Hamiltonian Path, Long Cycle, Long Path, and Min Cycle Cover all admit $5^d\cdot n^{\mathcal{O}(1)}$-time and polynomial space algorithms on graphs of treedepth $d$. The algorithms are randomized Monte Carlo with only false negatives.Comment: Presented at WG2020. 20 pages, 2 figure

Constraints on Nucleon Decay via "Invisible" Modes from the Sudbury Neutrino Observatory

Data from the Sudbury Neutrino Observatory have been used to constrain the lifetime for nucleon decay to ``invisible'' modes, such as n -> 3 nu. The analysis was based on a search for gamma-rays from the de-excitation of the residual nucleus that would result from the disappearance of either a proton or neutron from O16. A limit of tau_inv > 2 x 10^{29} years is obtained at 90% confidence for either neutron or proton decay modes. This is about an order of magnitude more stringent than previous constraints on invisible proton decay modes and 400 times more stringent than similar neutron modes.Comment: Update includes missing efficiency factor (limits change by factor of 2) Submitted to Physical Review Letter