Improved Bounds for Drawing Trees on Fixed Points with L-shaped Edges

Let $T$ be an $n$-node tree of maximum degree 4, and let $P$ be a set of $n$ points in the plane with no two points on the same horizontal or vertical line. It is an open question whether $T$ always has a planar drawing on $P$ such that each edge is drawn as an orthogonal path with one bend (an "L-shaped" edge). By giving new methods for drawing trees, we improve the bounds on the size of the point set $P$ for which such drawings are possible to: $O(n^{1.55})$ for maximum degree 4 trees; $O(n^{1.22})$ for maximum degree 3 (binary) trees; and $O(n^{1.142})$ for perfect binary trees. Drawing ordered trees with L-shaped edges is harder---we give an example that cannot be done and a bound of $O(n \log n)$ points for L-shaped drawings of ordered caterpillars, which contrasts with the known linear bound for unordered caterpillars.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Minimum Shared-Power Edge Cut

We introduce a problem called the Minimum Shared-Power Edge Cut (MSPEC). The input to the problem is an undirected edge-weighted graph with distinguished vertices s and t, and the goal is to find an s-t cut by assigning "powers" at the vertices and removing an edge if the sum of the powers at its endpoints is at least its weight. The objective is to minimize the sum of the assigned powers. MSPEC is a graph generalization of a barrier coverage problem in a wireless sensor network: given a set of unit disks with centers in a rectangle, what is the minimum total amount by which we must shrink the disks to permit an intruder to cross the rectangle undetected, i.e. without entering any disc. This is a more sophisticated measure of barrier coverage than the minimum number of disks whose removal breaks the barrier. We develop a fully polynomial time approximation scheme (FPTAS) for MSPEC. We give polynomial time algorithms for the special cases where the edge weights are uniform, or the power values are restricted to a bounded set. Although MSPEC is related to network flow and matching problems, its computational complexity (in P or NP-hard) remains open

EVALUATION OF PHYSICOCHEMICAL STANDARDIZATION PARAMETERS OF SOLENA AMPLEXICAULIS LEAF

Solena amplexicaulis, commonly called as the creeping cucumber, belongs to the family Cucurbitaceae. Traditional it is used as astringent, appetizer, carminative, cardiotonic, digestive, diuretic, expectorant, invigorating, purgative and stimulant. Plant also having antioxidant antidiabetic and antibacterial action. The leaves showed potent anti-inflammatory activity.The present study was carried out to establish physico-chemical parameters along with preliminary phytochemical screening of petroleum ether, chloroform, methanolic and aqueous extracts of Solena amplexicaulis leaf. Preliminary phytochemical screening of various extracts revealed the presence of carbohydrate, alkaloids, flavonoids, sterols, phenolic & tannins compounds. The physico-chemical parameters such as total, water soluble, acid insoluble and sulphated ash (2.2, 1.9, 1.17 and 1.3%w/w respectively) and loss on drying (10.0 %w/w), extractive values foaming and swelling index were studied.   These studies will be helpful in developing standards for quality, purity and sample identification of this plant. Keyword: Standardization, Solena amplexicaulis, physicochemical and phytochemical

Orthodontic Treatment Considerations in Pregnancy: An Insight

Introduction: This article presents an insight on little known fact regarding orthodontic treatment in pregnancy and to find literature support in favor regarding orthodontic treatment during pregnancy. Literature was reviewed extensively to get results dental and orthodontic treatment during pregnancy. Discussion: Nowadays there are many adult patients seekingorthodontic treatment because of increase in awareness. In these adult patients, there are many pregnant females coming to orthodontist for treatment or a lady getting pregnant during the treatment. ‘Can a pregnant woman continue with orthodontic treatment or can she start with orthodontic treatment during pregnancy?’ This is a difficult question to answer but ‘Yes’, pregnant women can go for orthodontic treatment but with precautions. Present article gives us the information how to go about the treatment in pregnant women, the precautions to be taken, effect of drugs and hormonal changes on orthodontic treatment. Conclusion: Pregnant women can go for orthodontic treatment but with some precaution and some systemic and local condition limit the treatment modalities