Approximation algorithms for Capacitated Facility Location Problem with Penalties

In this paper, we address the problem of capacitated facility location problem with penalties (CapFLPP) paid per unit of unserved demand. In case of uncapacitated FLP with penalties demands of a client are either entirely met or are entirely rejected and penalty is paid. In the uncapacitated case, there is no reason to serve a client partially. Whereas, in case of CapFLPP, it may be beneficial to serve a client partially instead of not serving at all and, pay the penalty for the unmet demand. Charikar et. al. \cite{charikar2001algorithms}, Jain et. al. \cite{jain2003greedy} and Xu- Xu \cite{xu2009improved} gave $3$, $2$ and $1.8526$ approximation, respectively, for the uncapacitated case . We present $(5.83 + \epsilon)$ factor for the case of uniform capacities and $(8.532 + \epsilon)$ factor for non-uniform capacities

Identification of factors determining the initiation of breastfeeding in postnatal women in a tertiary care centre: an observational study

Background: The WHO recommends that mothers worldwide to initiate breastfeeding within an hour of delivery to achieve optimal growth, development and health but the breastfeeding rates remain far below the recommended standards. The aim of this study was to find the prevalence of delay in initiation of breast feeding, to identify various factors which determine the initiation of breastfeeding and to correlate their association with delayed onset of breast feeding.Methods: Hundred and thirty six postnatal women, who delivered in Santosh Medical College and Hospital, Ghaziabad, were recruited in the study. They were interviewed after their informed consent using a pretested structured questionnaire. Socio-demographic and obstetric factors were compared between subjects who initiated breast feeding in less than and more than 1 hours. Frequencies were calculated for different variables. Data was statistically analyzed and p value of <0.05 was taken significant.Results: The prevalence of delay in initiation of breast feeding in our study was found to be 74.2% (n=101).The mean time of initiation of breast feeding was 18.43 hours. Significant association (p <0.05) was found in various sociodemographic, obstetrical and social factors.Conclusions: Identifying mothers at risk of delayed breastfeeding initiation should be the target for breastfeeding promotion during prenatal, antenatal as well as postnatal period. Public health officials and health care providers should consider interventions to promote and support early initiation of breast feeding

Genexpert test and endometrial histological findings in infertile women

Background: Infertility is a worldwide health problem with very definite physiological, psychological and social implications. According to studies, about 30% of infertility cases are due to the male factors, 40 to 50% have the origin of female factors and 20 to 30% of cases are caused by both male and female factors. Genital tuberculosis is among the main causes of female infertility. Due to its high prevalence, especially in developing countries, work-up of an infertile couple should include evaluation for tuberculosis irrespective of history or exposure. The objective of the present study is to find out the prevalence of genital tuberculosis in all females presenting with infertility in a tertiary care hospital over a given period of time, and diagnostic comparison of endometrial tuberculosis by GeneXpert and Histopathological examination (HPE).Methods: The prospective observational study was conducted from January 2016-June 2017.A total of 81 endometrial tissue samples were collected from the women, satisfying the inclusion and exclusion criteria.Results: GeneXpert scored negative in our study. On HPE, out of 81 patients, proliferative endometrium (anovulatory) was found in 34 cases (41.9%), non-specific endometritis in 1 case (1.23%) and 1 case (1.23%) was found positive for tubercular endometritis. Secretory endometrium was found in 45 cases (55.55%).Conclusions: Endometrial biopsy shows not only the tuberculous endometritis, but also gives additional information about hormone response of endometrium, local factors of endometrium concerning non-specific and specific infections and anovulatory cycles. Gene Expert if positive on endometrial biopsy is a reliable test for FGTB and treatment can be started on its basis

A 5-Approximation for Universal Facility Location

In this paper, we propose and analyze a local search algorithm for the Universal facility location problem. Our algorithm improves the approximation ratio of this problem from 5.83, given by Angel et al., to 5. A second major contribution of the paper is that it gets rid of the expensive multi operation that was a mainstay of all previous local search algorithms for capacitated facility location and universal facility location problem. The only operations that we require to prove the 5-approximation are add, open, and close. A multi operation is basically a combination of the open and close operations. The 5-approximation algorithm for the capacitated facility location problem, given by Bansal et al., also uses the multi operation. However, on careful observation, it turned out that add, open, and close operations are sufficient to prove a 5-factor for the problem. This resulted into an improved algorithm for the universal facility location problem, with an improved factor

FPT Approximations for Capacitated/Fair Clustering with Outliers

Clustering problems such as $k$-Median, and $k$-Means, are motivated from applications such as location planning, unsupervised learning among others. In such applications, it is important to find the clustering of points that is not ``skewed'' in terms of the number of points, i.e., no cluster should contain too many points. This is modeled by capacity constraints on the sizes of clusters. In an orthogonal direction, another important consideration in clustering is how to handle the presence of outliers in the data. Indeed, these clustering problems have been generalized in the literature to separately handle capacity constraints and outliers. To the best of our knowledge, there has been very little work on studying the approximability of clustering problems that can simultaneously handle both capacities and outliers. We initiate the study of the Capacitated $k$-Median with Outliers (C$k$MO) problem. Here, we want to cluster all except $m$ outlier points into at most $k$ clusters, such that (i) the clusters respect the capacity constraints, and (ii) the cost of clustering, defined as the sum of distances of each non-outlier point to its assigned cluster-center, is minimized. We design the first constant-factor approximation algorithms for C$k$MO. In particular, our algorithm returns a (3+\epsilon)-approximation for C$k$MO in general metric spaces, and a (1+\epsilon)-approximation in Euclidean spaces of constant dimension, that runs in time in time $f(k, m, \epsilon) \cdot |I_m|^{O(1)}$, where $|I_m|$ denotes the input size. We can also extend these results to a broader class of problems, including Capacitated k-Means/k-Facility Location with Outliers, and Size-Balanced Fair Clustering problems with Outliers. For each of these problems, we obtain an approximation ratio that matches the best known guarantee of the corresponding outlier-free problem.Comment: Abstract shortened to meet arxiv requirement

Insecticidal effects of aqueous extracts of wild pomegranate peel and seed (Punica granatum L.) against rose aphids, Macrosiphum rosaeformis

Efficacy of wild pomegranate (Punica granatum Linn.) fruit peel and seeds aqueous extract was evaluated for the control of common insect pests aphids (Macrosiphum rosaeformis) and for its influence on useful non-target predators viz., Coccinella septempunctata. Lethal doses of daru peel and seed suggested these became more toxic to aphids after 24 hr of exposure. A significant difference was obtained in percentage aphids reached to untreated leaves over peel extract treated leaves (23:57 and 23:77) and seed extract treated leaves (7:80 and 17:80) at 90 and 180 min time intervals in food choice assays. No significant effect was observed against Coccinella. LC50 values of daru peel and seed extracts along with mixture of three flavonoids (Kaempferol, Quercetin and Myricetin) were assessed at 48 hr values were 34.9, 4.7 and 0.6 mg/ml and at 72 hr these were 16.1, 0.000001 and 0.00001 mg/ml, respectively. In both the cases field bioassays showed affectivity till 7 DAT. Field data indicated that only X1(1 mg/ml) and X2 (0.1 mg/ml) concentrations of mixture were effective till 11 days after treatment. These are the first reports of the toxic effect of wild pomegranate (daru) fruit peel aqueous extract against M. rosaeformis, hence the study suggests possible usage of Punica granatum peel for the control of rose aphids