arXiv subjects

Priya Ranjan Sinha Mahapatra

Publications and source records attributed to Priya Ranjan Sinha Mahapatra.

5 recordsLinked to original sources

arXiv2024

Maximum-Width Rainbow-Bisecting Empty Annulus

Given a set of $n$ colored points with $k$ colors in the plane, we study the problem of computing a maximum-width rainbow-bisecting empty annulus (of objects specifically axis-parallel square, axis-parallel rectangle and circle) problem. We call a region rainbow if it contains at least one point of each color. The maximum-width rainbow-bisecting empty annulus problem asks to find an annulus $A$ of a particular shape with maximum possible width such that $A$ does not contain any input points and it bisects the input point set into two parts, each of which is a rainbow. We compute a maximum-width rainbow-bisecting empty axis-parallel square, axis-parallel rectangular and circular annulus in $O(n^3)$ time using $O(n)$ space, in $O(k^2n^2\log n)$ time using $O(n\log n)$ space and in $O(n^3)$ time using $O(n^2)$ space respectively.

cs.CG↗

arXiv2021

Efficient Reporting of Top-k Subset Sums

The "Subset Sum problem" is a very well-known NP-complete problem. In this work, a top-k variation of the "Subset Sum problem" is considered. This problem has wide application in recommendation systems, where instead of k best objects the k best subsets of objects with the lowest (or highest) overall scores are required. Given an input set R of n real numbers and a positive integer k, our target is to generate the k best subsets of R such that the sum of their elements is minimized. Our solution methodology is based on constructing a metadata structure G for a given n. Each node of G stores a bit vector of size n from which a subset of R can be retrieved. Here it is shown that the construction of the whole graph G is not needed. To answer a query, only implicit traversal of the required portion of G on demand is sufficient, which obviously gets rid of the preprocessing step, thereby reducing the overall time and space requirement. A modified algorithm is then proposed to generate each subset incrementally, where it is shown that it is possible to do away with the explicit storage of the bit vector. This not only improves the space requirement but also improves the asymptotic time complexity. Finally, a variation of our algorithm that reports only the top-k subset sums has been compared with an existing algorithm, which shows that our algorithm performs better both in terms of time and space requirement by a constant factor.

cs.DS↗

arXiv2018

Maximum-Width Empty Square and Rectangular Annulus

An annulus is, informally, a ring-shaped region, often described by two concentric circles. The maximum-width empty annulus problem asks to find an annulus of a certain shape with the maximum possible width that avoids a given set of $n$ points in the plane. This problem can also be interpreted as the problem of finding an optimal location of a ring-shaped obnoxious facility among the input points. In this paper, we study square and rectangular variants of the maximum-width empty anuulus problem, and present first nontrivial algorithms. Specifically, our algorithms run in $O(n^3)$ and $O(n^2 \log n)$ time for computing a maximum-width empty axis-parallel square and rectangular annulus, respectively. Both algorithms use only $O(n)$ space.

cs.CG↗

arXiv2017

Maximum-width Axis-Parallel Empty Rectangular Annulus

Given a set $P$ of $n$ points on $\mathbb R^{2}$, we address the problem of computing an axis-parallel empty rectangular annulus $A$ of maximum-width such that no point of $P$ lies inside $A$ but all points of $P$ must lie inside, outside and on the boundaries of two parallel rectangles forming the annulus $A$. We propose an $O(n^3)$ time and $O(n)$ space algorithm to solve the problem. In a particular case when the inner rectangle of an axis-parallel empty rectangular annulus reduces to an input point we can solve the problem in $O(n \log n)$ time and $O(n)$ space.

cs.CG↗

arXiv2016

No-hole $λ$-$L(k, k-1, \ldots, 2, 1)$-labeling for Square Grid

Given a fixed $k$ $\in$ $\mathbb{Z}^+$ and $λ$ $\in$ $\mathbb{Z}^+$, the objective of a $λ$-$L(k, k-1, \ldots, 2, 1)$-labeling of a graph $G$ is to assign non-negative integers (known as labels) from the set $\{0, \ldots, λ-1\}$ to the vertices of $G$ such that the adjacent vertices receive values which differ by at least $k$, vertices connected by a path of length two receive values which differ by at least $k-1$, and so on. The vertices which are at least $k+1$ distance apart can receive the same label. The smallest $λ$ for which there exists a $λ$-$L(k, k-1, \ldots, 2, 1)$-labeling of $G$ is known as the $L(k, k-1, \ldots, 2, 1)$-labeling number of $G$ and is denoted by $λ_k(G)$. The ratio between the upper bound and the lower bound of a $λ$-$L(k, k-1, \ldots, 2, 1)$-labeling is known as the approximation ratio. In this paper a lower bound on the value of the labeling number for square grid is computed and a formula is proposed which yields a $λ$-$L(k, k-1, \ldots, 2, 1)$-labeling of square grid, with approximation ratio at most $\frac{9}{8}$. The labeling presented is a no-hole one, i.e., it uses each label from $0$ to $λ-1$ at least once.

cs.DM↗