Approximation Algorithms for the Capacitated Domination Problem

We consider the {\em Capacitated Domination} problem, which models a service-requirement assignment scenario and is also a generalization of the well-known {\em Dominating Set} problem. In this problem, given a graph with three parameters defined on each vertex, namely cost, capacity, and demand, we want to find an assignment of demands to vertices of least cost such that the demand of each vertex is satisfied subject to the capacity constraint of each vertex providing the service. In terms of polynomial time approximations, we present logarithmic approximation algorithms with respect to different demand assignment models for this problem on general graphs, which also establishes the corresponding approximation results to the well-known approximations of the traditional {\em Dominating Set} problem. Together with our previous work, this closes the problem of generally approximating the optimal solution. On the other hand, from the perspective of parameterization, we prove that this problem is {\it W[1]}-hard when parameterized by a structure of the graph called treewidth. Based on this hardness result, we present exact fixed-parameter tractable algorithms when parameterized by treewidth and maximum capacity of the vertices. This algorithm is further extended to obtain pseudo-polynomial time approximation schemes for planar graphs

Total Roman {2}-domination in graphs

[EN] Given a graph G = (V, E), a function f: V -> {0, 1, 2} is a total Roman {2}-dominating function if every vertex v is an element of V for which f (v) = 0 satisfies that n-ary sumation (u)(is an element of N (v)) f (v) >= 2, where N (v) represents the open neighborhood of v, and every vertex x is an element of V for which f (x) >= 1 is adjacent to at least one vertex y is an element of V such that f (y) >= 1. The weight of the function f is defined as omega(f ) = n-ary sumation (v)(is an element of V) f (v). The total Roman {2}-domination number, denoted by gamma(t)({R2})(G), is the minimum weight among all total Roman {2}-dominating functions on G. In this article we introduce the concepts above and begin the study of its combinatorial and computational properties. For instance, we give several closed relationships between this parameter and other domination related parameters in graphs. In addition, we prove that the complexity of computing the value gamma(t)({R2})(G) is NP-hard, even when restricted to bipartite or chordal graphsCabrera García, S.; Cabrera Martinez, A.; Hernandez Mira, FA.; Yero, IG. (2021). Total Roman {2}-domination in graphs. Quaestiones Mathematicae. 44(3):411-444. https://doi.org/10.2989/16073606.2019.1695230S41144444

Amorphization threshold in Si-implanted strained SiGe alloy layers

The authors have examined the damage produced by Si-ion implantation into strained Si{sub 1{minus}x}Ge{sub x} epilayers. Damage accumulation in the implanted layers was monitored in situ by time-resolved reflectivity and measured by ion channeling techniques to determine the amorphization threshold in strained Si{sub 1{minus}x}Ge{sub x} (x = 0.16 and 0.29) over the temperature range 30--110 C. The results are compared with previously reported measurements on unstrained Si{sub 1{minus}x}Ge{sub x}, and with the simple model used to describe those results. They report here data which lend support to this model and which indicate that pre-existing strain does not enhance damage accumulation in the alloy layer

Socioeconomic status and diabetes technology use in youth with type 1 diabetes: a comparison of two funding models

Background Technology use, including continuous glucose monitoring (CGM) and insulin pump therapy, is associated with improved outcomes in youth with type 1 diabetes (T1D). In 2017 CGM was universally funded for youth with T1D in Australia. In contrast, pump access is primarily accessed through private health insurance, self-funding or philanthropy. The study aim was to investigate the use of diabetes technology across different socioeconomic groups in Australian youth with T1D, in the setting of two contrasting funding models. Methods A cross-sectional evaluation of 4957 youth with T1D aged <18 years in the national registry was performed to determine technology use. The Index of Relative Socio-Economic Disadvantage (IRSD) derived from Australian census data is an area-based measure of socioeconomic status (SES). Lower quintiles represent greater disadvantage. IRSD based on most recent postcode of residence was used as a marker of SES. A multivariable generalised linear model adjusting for age, diabetes duration, sex, remoteness classification, and location within Australia was used to determine the association between SES and device use. Results CGM use was lower in IRSD quintile 1 in comparison to quintiles 2 to 5 (p<0.001) where uptake across the quintiles was similar. A higher percentage of pump use was observed in the least disadvantaged IRSD quintiles. Compared to the most disadvantaged quintile 1, pump use progressively increased by 16% (95% CI: 4% to 31%) in quintile 2, 19% (6% to 33%) in quintile 3, 35% (21% to 50%) in quintile 4 and 51% (36% to 67%) in the least disadvantaged quintile 5. Conclusion In this large national dataset, use of diabetes technologies was found to differ across socioeconomic groups. For nationally subsidised CGM, use was similar across socioeconomic groups with the exception of the most disadvantaged quintile, an important finding requiring further investigation into barriers to CGM use within a nationally subsidised model. User pays funding models for pump therapy result in lower use with socioeconomic disadvantage, highlighting inequities in this funding approach. For the full benefits of diabetes technology to be realised, equitable access to pump therapy needs to be a health policy priority.Kate E. Lomax, Craig E. Taplin, Mary B. Abraham, Grant J. Smith, Aveni Haynes, Ella Zomer, Katrina L. Ellis, Helen Clapin, Sophia Zoungas, Alicia J. Jenkins, Jenny Harrington, Martin I. de Bock, Timothy W. Jones, and Elizabeth A. Davis, on behalf of the Australasian Diabetes Data Network, ADDN, study grou