Sasanka Roy

Bio: Sasanka Roy is an academic researcher from Indian Statistical Institute. The author has contributed to research in topics: Time complexity & Line segment. The author has an hindex of 13, co-authored 103 publications receiving 485 citations. Previous affiliations of Sasanka Roy include Indian Institute of Science & Tata Consultancy Services.

Shortest monotone descent path problem in polyhedral terrain

Abstract: Given a polyhedral terrain with n vertices, the shortest monotone descent path problem deals with finding the shortest path between a pair of points, called source (s) and destination (t) such that the path is constrained to lie on the surface of the terrain, and for every pair of points p=(x(p),y(p),z(p)) and q=(x(q),y(q),z(q)) on the path, if dist(s,p)=z(q), where dist(s,p) denotes the distance of p from s along the aforesaid path. This is posed as an open problem by Berg and Kreveld [M. de Berg, M. van Kreveld, Trekking in the Alps without freezing or getting tired, Algorithmica 18 (1997) 306-323]. We show that for some restricted classes of polyhedral terrain, the optimal path can be identified in polynomial time.

Querying for the Largest Empty Geometric Object in a Desired Location

Abstract: We study new types of geometric query problems defined as follows: given a geometric set $P$, preprocess it such that given a query point $q$, the location of the largest circle that does not contain any member of $P$, but contains $q$ can be reported efficiently. The geometric sets we consider for $P$ are boundaries of convex and simple polygons, and point sets. While we primarily focus on circles as the desired shape, we also briefly discuss empty rectangles in the context of point sets.

Property Testing and its connection to Learning and Approximation

Abstract: In this paper, we consider the question of determining whether a function f has property P or is e-far from any function with property P. A property testing algorithm is given a sample of the value of f on instances drawn according to some distribution. In some cases, it is also allowed to query f on instances of its choice. We study this question for different properties and establish some connections to problems in learning theory and approximation.In particular, we focus our attention on testing graph properties. Given access to a graph G in the form of being able to query whether an edge exists or not between a pair of vertices, we devise algorithms to test whether the underlying graph has properties such as being bipartite, k-Colorable, or having a p-Clique (clique of density p with respect to the vertex set). Our graph property testing algorithms are probabilistic and make assertions that are correct with high probability, while making a number of queries that is independent of the size of the graph. Moreover, the property testing algorithms can be used to efficiently (i.e., in time linear in the number of vertices) construct partitions of the graph that correspond to the property being tested, if it holds for the input graph.

Triangulating a simple polygon in linear time

Abstract: We give a deterministic algorithm for triangulating a simple polygon in linear time. The basic strategy is to build a coarse approximation of a triangulation in a bottom-up phase and then use the information computed along the way to refine the triangulation in a top-down phase. The main tools used are the polygon-cutting theorem, which provides us with a balancing scheme, and the planar separator theorem, whose role is essential in the discovery of new diagonals. Only elementary data structures are required by the algorithm. In particular, no dynamic search trees, of our algorithm.

Greed is good : approximating independent sets in sparse and bounded-degree graphs

Abstract: Theminimum-degree greedy algorithm, or Greedy for short, is a simple and well-studied method for finding independent sets in graphs. We show that it achieves a performance ratio of (Δ+2)/3 for approximating independent sets in graphs with degree bounded by Δ. The analysis yields a precise characterization of the size of the independent sets found by the algorithm as a function of the independence number, as well as a generalization of Turan's bound. We also analyze the algorithm when run in combination with a known preprocessing technique, and obtain an improved $$(2\bar d + 3)/5$$ performance ratio on graphs with average degree $$\bar d$$ , improving on the previous best $$(\bar d + 1)/2$$ of Hochbaum. Finally, we present an efficient parallel and distributed algorithm attaining the performance guarantees of Greedy.

Antioxidant therapies for wound healing: a clinical guide to currently commercially available products.

Abstract: Many facets of wound healing under redox control require a delicate balance between oxidative stress and antioxidants. While the normal physiology of wound healing depends on low levels of reactive oxygen species and oxidative stress, an overexposure to oxidative stress leads to impaired wound healing. Antioxidants are postulated to help control wound oxidative stress and thereby accelerate wound healing. Many antioxidants are available over the counter or by prescription, but only one, Medihoney®, has been specifically FDA approved for wound healing. Here we review the existing evidence for the use of antioxidants for wound healing, with a review of the pertinent animal and clinical studies. Natural products and naturally derived antioxidants are becoming more popular, and we specifically review the evidence for the use of naturally derived antioxidants in wound healing. Antioxidant therapy for wound healing is promising, but only few animal studies and even fewer clinical studies are available. Because only few products have undergone FDA approval, the consumer is advised to scrutinize them for purity and contaminants prior to use, and this may require direct contact with the companies that sell them. As a field of science, the use of antioxidants for wound healing is in its infancy, and future studies will better elucidate the role of antioxidants in wound healing.