Sandip Das

Bio: Sandip Das 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 5, co-authored 16 publications receiving 65 citations. Previous affiliations of Sandip Das include University of Burgundy.

Constrained minimum enclosing circle with center on a query line segment

Abstract: In this paper, we will study the problem of locating the center of the smallest enclosing circle of a set P of n points, where the center is constrained to lie on a query line segment The preprocessing time and space complexities of our proposed algorithm are O(nlogn) and O(n) respectively; the query time complexity is O(log^2n)

Constrained minimum enclosing circle with center on a query line segment

Abstract: In this paper, we will study the problem of locating the center of smallest enclosing circle of a set P of n points, where the center is constrained to lie on a query line segment. The preprocessing time and space complexities of our proposed algorithm are O(n log n) and 0(n) respectively; the query time complexity is O(log 2 n). We will use this method for solving the following problem proposed by Bose and Wang [3] - given r simple polygons with a total of m vertices along with the point set P, compute the smallest enclosing circle of P whose center lies in one of the r polygons. This can be solved in O(n log n+m log 2 n) time using our method in a much simpler way than [3]; the time complexity of the problem is also being improved.

Fast Computation of Smallest Enclosing Circle with Center on a Query Line Segment.

Abstract: Here we propose an efficient algorithm for computing the smallest enclosing circle whose center is constrained to lie on a query line segment. Our algorithm preprocesses a given set of n points P={p"1,p"2,...,p"n} such that for any query line or line segment L, it efficiently locates a point c on L that minimizes the maximum distance among the points in P from c. Roy et al. [S. Roy, A. Karmakar, S. Das, S.C. Nandy, Constrained minimum enclosing circle with center on a query line segment, in: Proc. of the 31st Mathematical Foundation of Computer Science, 2006, pp. 765-776] have proposed an algorithm that solves the query problem in O(log^2n) time using O(nlogn) preprocessing time and O(n) space. Our algorithm improves the query time to O(logn); but the preprocessing time and space complexities are both O(n^2).

Efficient algorithm for energy efficient broadcasting in linear radio networks

Abstract: Given a set S of n radio-stations located on a d-dimensional space, a source node s (∈ S) and an integer h (1 ≤ h ≤ |S| – 1), the h-hop broadcast range assignment problem deals with finding the range assignments for the members in S so that s can communicate with all other members in S in at most h-hops, and the total power consumption is minimum The problem is known to be NP-hard for d ≥ 2 We propose an O(n2) time algorithm for the one dimensional version (d = 1) of the problem This is an improvement over the existing results on this problem by a factor of h [5]

Some variations on constrained minimum enclosing circle problem

Abstract: Given a set P of n points and a straight line L, we study three important variations of minimum enclosing circle problem as follows:

The aligned K-center problem

Abstract: In this paper we study several instances of the alignedk-center problem where the goal is, given a set of points S in the plane and a parameter k ⩾ 1, to find k disks with centers on a line l such that their union covers S and the maximum radius of the disks is minimized. This problem is a constrained version of the well-known k-center problem in which the centers are constrained to lie in a particular region such as a segment, a line, or a polygon. We first consider the simplest version of the problem where the line l is given in advance; we can solve this problem in time O(n log2 n). In the case where only the direction of l is fixed, we give an O(n2log2 n)-time algorithm. When l is an arbitrary line, we give a randomized algorithm with expected running time O(n4log2 n). Then we present (1+e)-approximation algorithms for these three problems. When we denote T(k, e) = (k/e2+(k/e) log k) log(1/e), these algorithms run in O(n log k + T(k, e)) time, O(n log k + T(k, e)/e) time, and O(n log k + T(k, e)/e2) time, respectively. For k = O(n1/3/log n), we also give randomized algorithms with expected running times O(n + (k/e2) log(1/e)), O(n+(k/e3) log(1/e)), and O(n + (k/e4) log(1/e)), respectively.

A new cost-effective approach for battlefield surveillance in wireless sensor networks

Abstract: Assuring security (in the form of attacking mode as well as in safeguard mode) and at the same time keeping strong eye on the opposition’s status (position, quantity, availability) is the key responsibility of a commander in the battlefield. Battlefield surveillance is one of the strong applications of Wireless Sensor Networks (WSNs). A commander is not only liable to his above responsibilities, but also to manage his duties in an efficient way. For this reason, ensuring maximum destruction with minimum resources is a major concern of a commander in the battlefield. This paper focuses on the maximum destruction problem in military affairs. In [1] the authors proposed two novel algorithms (Maximum degree analysis and Maximum clique analysis) that ensure the efficiency and cost-effectiveness of the above problem. A comparative study explaining the number of resources required for commencing required level of destruction made to the opponents has been provided in the paper. In this paper the authors have come forward with another algorithm for the same problem. With the simulation studies and comparative analysis of the same example set the authors in this paper demonstrate the effectiveness (in both the quality and quantity) of the new method to be best among the three.

Minimum Separating Circle for Bichromatic Points in the Plane

Abstract: Consider two point sets in the plane, a red set of size n, and a blue set of size m. In this paper we show how to find the minimum separating circle, which is the smallest circle that contains all points of the red set and as few points as possible of the blue set in its interior. If multiple minimum separating circles exist our algorithm finds all of them. We also give an exact solution for finding the largest separating circle that contains all points of the red set and as few points as possible of the blue set in its interior. Our solutions make use of the farthest neighbor Voronoi Diagram of point sites.