Four-connected triangulations of planar point sets

In this paper, we consider the problem of determining in polynomial time whether a given planar point set $P$ of $n$ points admits 4-connected triangulation. We propose a necessary and sufficient condition for recognizing $P$, and present an $O(n^3)$ algorithm of constructing a 4-connected triangulation of $P$. Thus, our algorithm solves a longstanding open problem in computational geometry and geometric graph theory. We also provide a simple method for constructing a noncomplex triangulation of $P$ which requires $O(n^2)$ steps. This method provides a new insight to the structure of 4-connected triangulation of point sets.Comment: 35 pages, 35 figures, 5 reference

A linear time algorithm to remove winding of a simple polygon

AbstractIn this paper, we present a linear time algorithm to remove winding of a simple polygon P with respect to a given point q inside P. The algorithm removes winding by locating a subset of Jordan sequence that is in the proper order and uses only one stack

Trianthema portulacastrum L.: Traditional medicine in healthcare and biology

127-145Medicinal plants are the major folk and traditional medicine for the prevention of diseases worldwide. Trianthema portulacastrum L. (family: Aizoaceae), a small perennial weed, found in the America, Africa, India, and other regions of the world, and are extensively used not only as medicine but also as vegetable for its various health benefits. Phytochemical analysis of T. portulacastrum reveals the presence of alkaloids, phytosterols, terpenoids, saponins, flavonoids and phenolic compounds. In vitro and in vivo studies have demonstrated its pharmacological and biological activities. Different parts of T. portulacastrum L. are conventionally being used as analgesic, anti-pyretic, lipid lowering and microbicide agent; and protect liver and kidney from carcinogen, inflammation and oxidant chemicals