Sandip Das
Holes or Empty Pseudo-Triangles in Planar Point Sets.
Wed, 11/03/2010 - 16:01 — SomNambulAuthors: Sandip Das, Bhaswar B. Bhattacharya
Subjects: Combinatorics
AbstractLet $E(k, \ell)$ denote the smallest integer such that any set of at least
$E(k, \ell)$ points in the plane, no three on a line, contains either an empty
convex polygon with $k$ vertices or an empty pseudo-triangle with $\ell$
vertices. The existence of $E(k, \ell)$ for positive integers $k, \ell\geq 3$,
is the consequence of a result proved by Valtr [{\it Discrete and Computational
Geometry}, Vol. 37, 565--576, 2007].Recognizing the Largest Empty Circle and Axis-Parallel Rectangle in a Desired Location.
Tue, 04/06/2010 - 15:01 — SomNambulAuthors: Sandip Das, John Augustine, Anil Maheshwari, Subhas Nandy, Sasanka Roy, Swami Sarvattomananda
Subjects: Computational Geometry
AbstractIn this paper, we study the query version of the largest empty space
recognition problem. Here, a set of $n$ points $P$ is given in a bounded 2D
region. The objective is to preprocess $P$ such that given any arbitrary query
point $q$, the largest empty region of some desired shape that contains $q$ but
does not contain any point in $P$ can be reported efficiently.On Finding Non-dominated Points using Compact Voronoi Diagrams.
Mon, 09/07/2009 - 22:13 — SomNambulAuthors: Binay Bhattacharya, Arijit Bishnu, Otfried Cheong, Sandip Das, Arindam Karmakar, Jack Snoeyink
Subjects: Computational Geometry
AbstractWe discuss in this paper a method of finding skyline or non-dominated points
in a set $P$ of $n_P$ points with respect to a set $S$ of $n_S$ sites. A point
$p_i \in P$ is non-dominated if and only if for each $p_j \in P$, $j \not= i$,
there exists at least one point $s \in S$ that is closer to $p_i$ than $p_j$.
We reduce this problem of determining non-dominated points to the problem of
finding sites that have non-empty cells in an additive Voronoi diagram with a
convex distance function.
User login
