The Traveling Salesman Problem Under Squared Euclidean Distances

Let $P$ be a set of points in $\mathbb{R}^d$, and let $\alpha \ge 1$ be a real number. We define the distance between two points $p,q\in P$ as $|pq|^{\alpha}$, where $|pq|$ denotes the standard Euclidean distance between $p$ and $q$. We denote the traveling salesman problem under this distance function by TSP($d,\alpha$). We design a 5-approximation algorithm for TSP(2,2) and generalize this result to obtain an approximation factor of $3^{\alpha-1}+\sqrt{6}^{\alpha}/3$ for $d=2$ and all $\alpha\ge2$. We also study the variant Rev-TSP of the problem where the traveling salesman is allowed to revisit points. We present a polynomial-time approximation scheme for Rev-TSP$(2,\alpha)$ with $\alpha\ge2$, and we show that Rev-TSP$(d, \alpha)$ is APX-hard if $d\ge3$ and $\alpha>1$. The APX-hardness proof carries over to TSP$(d, \alpha)$ for the same parameter ranges.Comment: 12 pages, 4 figures. (v2) Minor linguistic change

Non-Destructive Testing Techniques for Corrosion Assessment in Reinforced Concrete Structures in Kenya

Deterioration of concrete structures is inevitable due to the fact that it is subjected to deterring environmental factors. Therefore, inspection and maintenance of these structures should be done to ensure their serviceability. Many concrete structures have been constructed in Kenya. A survey of some of the existing multi-storey buildings shows that even some of the old ones are in good condition; examples are the Norfork Hotel, Sarova Stanley Hotel and the railway bridges built in early 1900s. Yet, ageing structures require periodic monitoring to check their serviceability. Currently, inspection of most structures is done solely by simple visual means which is not always adequate. In order to enhance reliable assessment of structures, the present research introduces non-destructive testing (NDT) techniques for corrosion damage diagnosis in Kenyan concrete structures. Visual inspection is followed by half-cell potential measurements, carbonation tests and chloride tests. Laboratory analysis as well as field testing shows that NDT techniques provide safe, fast and reliable tools for the assessment of structural integrity. Keywords: Reinforced Concrete, Deterioration, Inspection, Non-destructive testin

Scheduling divisible loads with time and cost constraints

In distributed computing, divisible load theory provides an important system model for allocation of data-intensive computations to processing units working in parallel. The main task is to define how a computation job should be split into parts, to which processors those parts should be allocated and in which sequence. The model is characterized by multiple parameters describing processor availability in time, transfer times of job parts to processors, their computation times and processor usage costs. The main criteria are usually the schedule length and cost minimization. In this paper, we provide the generalized formulation of the problem, combining key features of divisible load models studied in the literature, and prove its NP-hardness even for unrestricted processor availability windows. We formulate a linear program for the version of the problem with a fixed number of processors. For the case with an arbitrary number of processors, we close the gaps in the study of special cases, developing efficient algorithms for single criterion and bicriteria versions of the problem, when transfer times are negligible

Nutrient availability controls the impact of mammalian herbivores on soil carbon and nitrogen pools in grasslands

Grasslands are subject to considerable alteration due to human activities globally, including widespread changes in populations and composition of large mammalian herbivores and elevated supply of nutrients. Grassland soils remain important reservoirs of carbon (C) and nitrogen (N). Herbivores may affect both C and N pools and these changes likely interact with increases in soil nutrient availability. Given the scale of grassland soil fluxes, such changes can have striking consequences for atmospheric C concentrations and the climate. Here, we use the Nutrient Network experiment to examine the responses of soil C and N pools to mammalian herbivore exclusion across 22 grasslands, under ambient and elevated nutrient availabilities (fertilized with NPK + micronutrients). We show that the impact of herbivore exclusion on soil C and N pools depends on fertilization. Under ambient nutrient conditions, we observed no effect of herbivore exclusion, but under elevated nutrient supply, pools are smaller upon herbivore exclusion. The highest mean soil C and N pools were found in grazed and fertilized plots. The decrease in soil C and N upon herbivore exclusion in combination with fertilization correlated with a decrease in aboveground plant biomass and microbial activity, indicating a reduced storage of organic matter and microbial residues as soil C and N. The response of soil C and N pools to herbivore exclusion was contingent on temperature – herbivores likely cause losses of C and N in colder sites and increases in warmer sites. Additionally, grasslands that contain mammalian herbivores have the potential to sequester more N under increased temperature variability and nutrient enrichment than ungrazed grasslands. Our study highlights the importance of conserving mammalian herbivore populations in grasslands worldwide. We need to incorporate local-scale herbivory, and its interaction with nutrient enrichment and climate, within global-scale models to better predict land–atmosphere interactions under future climate change.National Science Foundation Research Coordination Network, Long Term Ecological Research, Institute on the Environment, Strategic Resources of the Netherlands Institute of Ecology, Research Foundation Flanders, VENI grant, NWO-RUBICON grant, NWO-VENI grant, German Centre for Integrative Biodiversity Research, German Research Foundation (FZT 118).http://wileyonlinelibrary.com/journal/gcbpm2021Mammal Research InstituteZoology and Entomolog

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