Quantum Optimization Problems

Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a quantum optimization problem using polynomial-time quantum computations and introduces the notion of an ``universal'' quantum optimization problem similar to a classical ``complete'' optimization problem. We exhibit a canonical quantum optimization problem that is universal for the class of polynomial-time quantum optimization problems. We show in a certain relativized world that all quantum optimization problems cannot be approximated closely by quantum polynomial-time computations. We also study the complexity of quantum optimization problems in connection to well-known complexity classes.Comment: date change

Worst case and probabilistic analysis of the 2-Opt algorithm for the TSP

2-Opt is probably the most basic local search heuristic for the TSP. This heuristic achieves amazingly good results on “real world” Euclidean instances both with respect to running time and approximation ratio. There are numerous experimental studies on the performance of 2-Opt. However, the theoretical knowledge about this heuristic is still very limited. Not even its worst case running time on 2-dimensional Euclidean instances was known so far. We clarify this issue by presenting, for every p∈N , a family of L p instances on which 2-Opt can take an exponential number of steps. Previous probabilistic analyses were restricted to instances in which n points are placed uniformly at random in the unit square [0,1]2, where it was shown that the expected number of steps is bounded by O~(n10) for Euclidean instances. We consider a more advanced model of probabilistic instances in which the points can be placed independently according to general distributions on [0,1] d , for an arbitrary d≥2. In particular, we allow different distributions for different points. We study the expected number of local improvements in terms of the number n of points and the maximal density ϕ of the probability distributions. We show an upper bound on the expected length of any 2-Opt improvement path of O~(n4+1/3⋅ϕ8/3) . When starting with an initial tour computed by an insertion heuristic, the upper bound on the expected number of steps improves even to O~(n4+1/3−1/d⋅ϕ8/3) . If the distances are measured according to the Manhattan metric, then the expected number of steps is bounded by O~(n4−1/d⋅ϕ) . In addition, we prove an upper bound of O(ϕ√d) on the expected approximation factor with respect to all L p metrics. Let us remark that our probabilistic analysis covers as special cases the uniform input model with ϕ=1 and a smoothed analysis with Gaussian perturbations of standard deviation σ with ϕ∼1/σ d

Promoting gender, equity, human rights and ethnic equality in neglected tropical disease programmes.

Limited attention to tackling neglected tropical diseases (NTDs) through the lenses of gender, equity, ethnicity and human rights inadvertently undermines progress due to the exclusion of subgroups in populations living in conditions of vulnerability. Supporting national NTD programmes to make equity analysis part of their routine activities and revitalising intersectoral collaboration will be essential to achieve effective, sustainable service delivery with a person-centred approach. Gender, equity, human rights and ethnic equality for NTD programmes should therefore be incorporated in multisectoral engagements

Mathematical modelling of lymphatic filariasis elimination programmes in India: Required duration of mass drug administration and post-treatment level of infection indicators

Background: India has made great progress towards the elimination of lymphatic filariasis. By 2015, most endemic districts had completed at least five annual rounds of mass drug administration (MDA). The next challenge is to determine when MDA can be stopped. We performed a simulation study with the individual-based model LYMFASIM to help clarify this. Methods: We used a model-variant for Indian settings. We considered different hypotheses on detectability of antigenaemia (Ag) in relation to underlying adult worm burden, choosing the most likely hypothesis by comparing the model predicted association between community-level microfilaraemia (Mf) and antigenaemia (Ag) prevalence levels to observed data (collated from literature). Next, we estimated how long MDA must be continued in order to achieve elimination in different transmission settings and what Mf and Ag prevalence may still remain 1 year after the last required MDA round. The robustness of key-outcomes was assessed in a sensitivity analysis. Results: Our model matched observed data qualitatively well when we assumed an Ag detection rate of 50 % for single worm infections, which increases with the number of adult worms (modelled by relating detection to the presence of female worms). The required duration of annual MDA increased with higher baseline endemicity and lower coverage (varying between 2 and 12 rounds), while the remaining residual infection 1 year after the last required treatment declined with transmission intensity. For low and high transmission settings, the median residual infection levels were 1.0 % and 0.4 % (Mf prevalence in the 5+ population), and 3.5 % and 2.0 % (Ag prevalence in 6-7 year-old children). Conclusion: To achieve elimination in high transmission settings, MDA must be continued longer and infection levels must be reduced to lower levels than in low-endemic communities. Although our simulations were for Indian settings, qualitatively similar patterns are also expected in other areas. This should be taken into account in decision algorithms to define whether MDA can be interrupted. Transmission assessment surveys should ideally be targeted to communities with the highest pre-control transmission levels, to minimize the risk of programme failure

Optimal Satisfiability for Propositional Calculi and Constraint Satisfaction Problems

We consider the problems of finding the lexicographically minimal (or maximal) satisfying assignment of propositional formulas for different restricted classes of formulas. It turns out that for each class from our framework, these problems are either polynomial time solvable or complete for OptP. We also consider the problem of deciding if in the optimal assignment the largest variable gets value 1. We show that this problem is either in P or P^NP complete

Diagnosing performance bottlenecks in emerging petascale applications

Cutting-edge science and engineering applications require petascale computing. It is, however, a significant challenge to use petascale computing platforms effectively. Consequently, there is a critical need for performance tools that enable scientists to understand impediments to performance on emerging petascale systems. In this paper, we describe HPCToolkit—a suite of multi-platform tools that supports sampling-based analysis of application performance on emerging petascale platforms. HPCToolkit uses sampling to pinpoint and quantify both scaling and node performance bottlenecks. We study several emerging petascale applications on the Cray XT and IBM BlueGene/P platforms and use HPCToolkit to identify specific source lines — in their full calling context — associated with performance bottlenecks in these codes. Such information is exactly what application developers need to know to improve their applications to take full advantage of the power of petascale systems

The Zig Zag Railway New South Wales [picture] /

Title devised by cataloguer from inscriptions.; Condition: Folds.; Inscriptions: "The Zig Zag. 686"--Printed on image lower left; "Kerry Photo. Sydney."--Printed on image lower right.; Part of the collection: Charles Kerry collection of New South Wales views.; Also available online http://nla.gov.au/nla.pic-vn6100794