Structural parameterizations for boxicity

The boxicity of a graph $G$ is the least integer $d$ such that $G$ has an intersection model of axis-aligned $d$-dimensional boxes. Boxicity, the problem of deciding whether a given graph $G$ has boxicity at most $d$, is NP-complete for every fixed $d \ge 2$. We show that boxicity is fixed-parameter tractable when parameterized by the cluster vertex deletion number of the input graph. This generalizes the result of Adiga et al., that boxicity is fixed-parameter tractable in the vertex cover number. Moreover, we show that boxicity admits an additive $1$-approximation when parameterized by the pathwidth of the input graph. Finally, we provide evidence in favor of a conjecture of Adiga et al. that boxicity remains NP-complete when parameterized by the treewidth.Comment: 19 page

Frequency of Aspirating Gastric Tubes for Patients Receiving Enteral Nutrition in the ICU: A Randomised Controlled Trial

Background: Enteral nutrition (EN) tolerance is often monitored by aspirating stomach contents by syringe at prescribed intervals. No studies have been conducted to assess the most appropriate time interval for aspirating gastric tubes. We compared gastric tube aspirations every 4 hours (usual care) with a variable regimen (up to every 8 hours aspirations).Methods: This randomized controlled trial (RCT) enrolled patients who stayed in the intensive care unit (ICU) for >48 hours, had a gastric tube, and were likely to receive EN for 3 or more days. Patients were randomized (computer-generated randomization) to either the control (every 4 hours) or intervention group (variable regimen). The primary outcome was number of gastric tube aspirations per day from randomization until EN was ceased or up to 2 weeks postrandomization.Results: Following Institutional Ethics Committee approval, 357 patients were recruited (control group, n = 179; intervention group, n = 178). No differences were found in age, sex, worst APACHE II score, or time to start of EN. In the intention-to-treat analysis, the intervention group had fewer tube aspirations per day (3.4 versus 5.4 in the control group, P < .001). Vomiting/regurgitation was increased in the intervention group (2.1% versus 3.6%, P = .02). There were no other differences in complications.Conclusion: This is the first RCT to examine the frequency of gastric tube aspirations. The frequency of gastric tube aspirations was reduced in the variable-regimen group with no increase in risk to the patient. Reducing the frequency of aspirations saves nursing time, decreases risk of contamination of feeding circuit, and minimizes risk of body fluid exposure