arXiv subjects

Sanjib Sadhu

Publications and source records attributed to Sanjib Sadhu.

5 recordsLinked to original sources

arXiv2025

Asymmetric Separation Problem for Bichromatic Point Set

We study the Generalized Red-Blue Annulus Cover problem for two sets of points, red ($R$) and blue ($B$), where each point $p \in R\cup B$ is associated with a positive penalty ${\cal P}(p)$. The red points have non-covering penalties, and the blue points have covering penalties. The objective is to compute an annulus (either a rectangular or a circular) $\cal A$ such that the value of the function ${\cal P}({R}^{out}) + {\cal P}({ B}^{in})$ is minimum, where ${R}^{out} \subseteq {R}$ is the set of red points not covered by ${\cal A}$, and ${B}^{in} \subseteq {B}$ is the set of blue points covered by $\cal A$. We study the problem for various types of axis-parallel rectangular annulus and circular annulus in one and two dimensions. We also study a restricted version of the rectangular annulus cover problem, where the center of the annulus is constrained to lie on a given horizontal line $L$. We design a polynomial-time algorithm for each type of annulus.

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arXiv2019

Corrigendum to: "Linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares", Theoretical Computer Science 769 (2019) 63--74

In the paper "Linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares", TCS Volume 769 (2019), pages 63--74, the LHIT problem is proposed as follows: For a given set of non-intersecting line segments ${\cal L} = \{\ell_1, \ell_2, \ldots, \ell_n\}$ in $I\!\!R^2$, compute two axis-parallel congruent squares ${\cal S}_1$ and ${\cal S}_2$ of minimum size whose union hits all the line segments in $\cal L$, and a linear time algorithm was proposed. Later it was observed that the algorithm has a bug. In this corrigendum, we corrected the algorithm. The time complexity of the corrected algorithm is $O(n^2)$.

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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.

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arXiv2017

A linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares

This paper discusses the problem of covering and hitting a set of line segments $\cal L$ in ${\mathbb R}^2$ by a pair of axis-parallel squares such that the side length of the larger of the two squares is minimized. We also discuss the restricted version of covering, where each line segment in $\cal L$ is to be covered completely by at least one square. The proposed algorithm for the covering problem reports the optimum result by executing only two passes of reading the input data sequentially. The algorithm proposed for the hitting and restricted covering problems produces optimum result in $O(n)$ time. All the proposed algorithms are in-place, and they use only $O(1)$ extra space. The solution of these problems also give a $\sqrt{2}$ approximation for covering and hitting those line segments $\cal L$ by two congruent disks of minimum radius with same computational complexity.

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arXiv2015

Approximation algorithms for the two-center problem of convex polygon

Given a convex polygon $P$ with $n$ vertices, the two-center problem is to find two congruent closed disks of minimum radius such that they completely cover $P$. We propose an algorithm for this problem in the streaming setup, where the input stream is the vertices of the polygon in clockwise order. It produces a radius $r$ satisfying $r\leq2r_{opt}$ using $O(1)$ space, where $r_{opt}$ is the optimum solution. Next, we show that in non-streaming setup, we can improve the approximation factor by $r\leq 1.84 r_{opt}$, maintaining the time complexity of the algorithm to $O(n)$, and using $O(1)$ extra space in addition to the space required for storing the input.

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