Polynomial Kernels for Weighted Problems

Kernelization is a formalization of efficient preprocessing for NP-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial kernelizations for Subset Sum and Knapsack when parameterized by the number $n$ of items. We answer both questions affirmatively by using an algorithm for compressing numbers due to Frank and Tardos (Combinatorica 1987). This result had been first used by Marx and V\'egh (ICALP 2013) in the context of kernelization. We further illustrate its applicability by giving polynomial kernels also for weighted versions of several well-studied parameterized problems. Furthermore, when parameterized by the different item sizes we obtain a polynomial kernelization for Subset Sum and an exponential kernelization for Knapsack. Finally, we also obtain kernelization results for polynomial integer programs

General graviton exchange graph for four point functions in the AdS/CFT correspondence

In this note we explicitly compute the graviton exchange graph for scalar fields with arbitrary conformal dimension \Delta in arbitrary spacetime dimension d. This results in an analytical function in \Delta as well as in d.Comment: 14 pages, 2 figure

Crossing Paths with Hans Bodlaender:A Personal View on Cross-Composition for Sparsification Lower Bounds

On the occasion of Hans Bodlaender’s 60th birthday, I give a personal account of our history and work together on the technique of cross-composition for kernelization lower bounds. I present several simple new proofs for polynomial kernelization lower bounds using cross-composition, interlaced with personal anecdotes about my time as Hans’ PhD student at Utrecht University. Concretely, I will prove that Vertex Cover, Feedback Vertex Set, and the H-Factor problem for every graph H that has a connected component of at least three vertices, do not admit kernels of (formula presented) bits when parameterized by the number of vertices n for any (formula presented), unless (formula presented). These lower bounds are obtained by elementary gadget constructions, in particular avoiding the use of the Packing Lemma by Dell and van Melkebeek.</p

Stochastic make-to-stock inventory deployment problem: an endosymbiotic psychoclonal algorithm based approach

Integrated steel manufacturers (ISMs) have no specific product, they just produce finished product from the ore. This enhances the uncertainty prevailing in the ISM regarding the nature of the finished product and significant demand by customers. At present low cost mini-mills are giving firm competition to ISMs in terms of cost, and this has compelled the ISM industry to target customers who want exotic products and faster reliable deliveries. To meet this objective, ISMs are exploring the option of satisfying part of their demand by converting strategically placed products, this helps in increasing the variability of product produced by the ISM in a short lead time. In this paper the authors have proposed a new hybrid evolutionary algorithm named endosymbiotic-psychoclonal (ESPC) to decide what and how much to stock as a semi-product in inventory. In the proposed theory, the ability of previously proposed psychoclonal algorithms to exploit the search space has been increased by making antibodies and antigen more co-operative interacting species. The efficacy of the proposed algorithm has been tested on randomly generated datasets and the results compared with other evolutionary algorithms such as genetic algorithms (GA) and simulated annealing (SA). The comparison of ESPC with GA and SA proves the superiority of the proposed algorithm both in terms of quality of the solution obtained and convergence time required to reach the optimal/near optimal value of the solution

Compact Labelings For Efficient First-Order Model-Checking

We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the graphs of every class that is \emph{nicely locally cwd-decomposable}. This notion generalizes that of a \emph{nicely locally tree-decomposable} class. The graphs of such classes can be covered by graphs of bounded \emph{clique-width} with limited overlaps. We also consider such labelings for \emph{bounded} first-order formulas on graph classes of \emph{bounded expansion}. Some of these results are extended to counting queries

The Minimum Shared Edges Problem on Grid-like Graphs

We study the NP-hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route $p$ paths from a start vertex to a target vertex in a given graph while using at most $k$ edges more than once. We show that MSE can be decided on bounded (i.e. finite) grids in linear time when both dimensions are either small or large compared to the number $p$ of paths. On the contrary, we show that MSE remains NP-hard on subgraphs of bounded grids. Finally, we study MSE from a parametrised complexity point of view. It is known that MSE is fixed-parameter tractable with respect to the number $p$ of paths. We show that, under standard complexity-theoretical assumptions, the problem parametrised by the combined parameter $k$, $p$, maximum degree, diameter, and treewidth does not admit a polynomial-size problem kernel, even when restricted to planar graphs

Best practice in the management of online sex offending

Our report sets out the outcomes from reviews of the relevant literature, and a series of consultations held by IWG_OSO, with participation from practitioners and researchers working in the field of child protection and online sex offending. Online sex offending. Internationally, researchers and practitioners have documented rises in the scale and impact of online sex offending, including the grooming of minors and vulnerable people for sexual purposes, sexual trafficking, and most dramatically, child sexual exploitation material and the related offences of its possession, production and distribution. Such a ‘high volume crime’ outweighs the capacity for effective management and prevention through the strategies and resources currently being used. This makes prosecution and case management increasingly difficult. Challenges to good practice.Without empirically based good practice, professionals are unable to deal effectively with the prevention of online sex offending, risk-management, and treatment decisions. This creates major limitations for the police, courts, probation, child protection, and other services, which are working to protect and safeguard children from online child sexual offenders, and to manage and prevent offending behaviours. Current issues and possible solutions. A series of current issues were highlighted, with possible solutions offered by IWG_OSO stakeholders. These included suggestions for changes in: international policy on CSEM offending; working with the internet industry; policing issues; research concerns; risk assessment and treatment developments; inter-agency and multi-disciplinary collaboration; barriers to change; and preventative methods.Conclusions.1. An increase in arresting and prosecuting offenders; 2. An increase in earlier interventions and primary and secondary prevention; 3. An increase in research to aid risk assessments, treatment options and prevention approaches; 4. An increase in international collaboration and consistency in applying learning to policy and practice

Reduction of low- and high-grade cervical abnormalities associated with high uptake of the HPV bivalent vaccine in Scotland

In Scotland, a national HPV immunisation programme began in 2008 for 12-13 year olds, with a catch-up campaign from 2008-2011 for those under the age of 18. To monitor the impact of HPV immunisation on cervical disease at the population level, a programme of national surveillance was established.  We analysed colposcopy data from a cohort of women born between 1988-1992 who entered the Scottish Cervical Screening Programme (SCSP) and were aged 20-21 in 2008-2012.  By linking datasets from the SCSP and colposcopy services, we observed a significant reduction in diagnoses of cervical intraepithelial neoplasia 1 (CIN 1) (RR 0.71, 95% CI 0.58 to 0.87, p=0.0008), CIN 2 (RR 0.5, 95% CI 0.4, 0.63, p<0.0001) and CIN 3 (RR 0.45, 95% CI 0.35 to 0.58, p< 0.0001) for women who received 3 doses of vaccine compared with unvaccinated women.  To our knowledge, this is one of the first studies to show a reduction of low and high grade cervical intraepithelial neoplasia associated with high uptake of the HPV bivalent vaccine at the population level. These data are very encouraging for countries that have achieved high HPV vaccine uptake