Parameterizing Path Partitions

We study the algorithmic complexity of partitioning the vertex set of a given (di)graph into a small number of paths. The Path Partition problem (PP) has been studied extensively, as it includes Hamiltonian Path as a special case. The natural variants where the paths are required to be either \emph{induced} (Induced Path Partition, IPP) or \emph{shortest} (Shortest Path Partition, SPP), have received much less attention. Both problems are known to be NP-complete on undirected graphs; we strengthen this by showing that they remain so even on planar bipartite directed acyclic graphs (DAGs), and that SPP remains \NP-hard on undirected bipartite graphs. When parameterized by the natural parameter ``number of paths'', both SPP and IPP are shown to be W{1}-hard on DAGs. We also show that SPP is in \XP both for DAGs and undirected graphs for the same parameter, as well as for other special subclasses of directed graphs (IPP is known to be NP-hard on undirected graphs, even for two paths). On the positive side, we show that for undirected graphs, both problems are in FPT, parameterized by neighborhood diversity. We also give an explicit algorithm for the vertex cover parameterization of PP. When considering the dual parameterization (graph order minus number of paths), all three variants, IPP, SPP and PP, are shown to be in FPT for undirected graphs. We also lift the mentioned neighborhood diversity and dual parameterization results to directed graphs; here, we need to define a proper novel notion of directed neighborhood diversity. As we also show, most of our results also transfer to the case of covering by edge-disjoint paths, and purely covering.Comment: 27 pages, 8 figures. A short version appeared in the proceedings of the CIAC 2023 conferenc

Parameterizing Path Partitions

International audienc

Determinants of awareness on pictorial health warnings on tobacco products in an Eastern state of India

Background: Pictorial health warnings (PHW) are an effective strategy to deter or reduce tobacco use. This study was conducted to determine the level of awareness of PHWs on tobacco products and their correlates among adults attending the outpatient department (OPD) of a tertiary care facility in Eastern India. Materials and Methods: This cross-sectional study was conducted over a period of 3 months among 307 patients aged 18 years to 65 years. A pre-tested semi-structured questionnaire was used for the collection of data and inferential statistics were performed using JAMOVI version 2.3.21. Results: About 84% (95% CI, 78.9-87.2) of the participants were aware of PHW on tobacco products, 82.4% (95% CI, 77.8-86.3) for smoked forms and 51.8% (95% CI, 46.2-57.3) for smokeless forms. More than half of the participants felt that the current PHW were ineffective. Male [AOR, 3.13; 95% CI, 1.33-7.37], being educated [AOR, 3.37; 95% CI, 1.29-8.76], employment [AOR, 5.65; 95% CI, 1.21-26.30] and ever-tobacco use [AOR, 3.23; 95% CI, 1.43-7.2] were found to be independent correlates of PHW awareness for smoked tobacco products, whereas as being male [AOR, 2.01; 95% CI, 1.02-3.95] and being young (18-30 years) [AOR, 2.51; 95% CI, 1.08-5.84] were found to be the independent predictors of PHW awareness for smokeless tobacco products (SLT). Conclusion: Four out of every five individuals were aware of pictorial health warnings (PHW) on tobacco products; however, it was much less for SLT compared to smoked tobacco products. Male, being educated, employment and ever-tobacco use were independent correlates of awareness for the smoked form of tobacco products, whereas being young (18-30 years) was an independent predictor of awareness for SLT

3rd National Conference on Image Processing, Computing, Communication, Networking and Data Analytics

This volume contains contributed articles presented in the conference NCICCNDA 2018, organized by the Department of Computer Science and Engineering, GSSS Institute of Engineering and Technology for Women, Mysore, Karnataka (India) on 28th April 2018