For α > 1, an α-approximate (bi-)kernel is a polynomial-time algorithm that takes as input an instance (I, k) of a problem Q and outputs an instance (I , k ) (of a problem Q ) of size bounded by a function of k such that, for every c ≥ 1, a c-approximate solution for the new instance can be turned into a (c · α)-approximate solution of the original instance in polynomial time. This framework of lossy kernelization was recently introduced by Lokshtanov et al. We study Connected Dominating Set (and its distance-r variant) parameterized by solution size on sparse graph classes like biclique-free graphs, classes of bounded expansion, and nowhere dense classes. We prove that for every α > 1, Connected Dominating Set admits a polynomial-size α-approximate (bi-)kernel on all the aforementioned classes. Our results are in sharp contrast to the kernelization complexity of Connected Dominating Set, which is known to not admit a polynomial kernel even on 2-degenerate graphs and graphs of bounded expansion, unless NP ⊆ coNP/poly. We complement our results by the following conditional lower bound. We show that if a class C is somewhere dense and closed under taking subgraphs, then for some value of r ∈ N there cannot exist an α-approximate bi-kernel for the (Connected) Distance-r Dominating Set problem on C for any α > 1 (assuming the Gap Exponential Time Hypothesis).

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Introduction: Typhoid fever is a life-threatening systemic infection occurring in developing countries like India. The presenting signs and symptoms of typhoid fever in children differ from adults. Some studies indicate reemergence of sensitivity of Salmonella with chloramphenicol. Method: 164 children between 1-12 years of age with suspected enteric fever were enrolled in the study. Out of these, 73 patients were diagnosed as enteric fever and clinical features were compared among different age groups. Antibiotic sensitivity profile was also studied in blood culture positive patients. Results: Abdominal distension were significantly more commonly seen in children less than 5 years while nausea, constipation and blood in stool were completely absent in this age group. Abdominal pain and headache were significantly more in children more 5 years than compared to it younger group. The sensitivity for classical drugs Chloramphenicol, Ampicillin and Cotrimoxazole was found to be 70%, 80% and 47.5%, respectively. Conclusion: Clinical profile of enteric fever in children differ with age. There is re-emergence of sensitivity of Salmonella typhi for chloramphenicol, ampicillin and Cotrimoxazole in blood culture.