Rahnuma Islam Nishat
University of Victoria
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Publication
Featured researches published by Rahnuma Islam Nishat.
Journal of Graph Algorithms and Applications | 2011
Debajyoti Mondal; Rahnuma Islam Nishat; Md. Saidur Rahman; Muhammad Jawaherul Alam
A straight-line grid drawing of a plane graph G is a planar drawing of G, where each vertex is drawn at a grid point of an integer grid and each edge is drawn as a straight-line segment. The area of such a drawing is the area of the smallest axis-aligned rectangle on the grid which encloses the drawing. A minimum-area drawing of a plane graph G is a straight-line grid drawing of G where the area of the drawing is the minimum. Although it is NP-hard to find minimum-area drawings for general plane graphs, in this paper we obtain minimumarea drawings for plane 3-trees in polynomial time. Furthermore, we show a ⌊ 2n 3 − 1⌋ × 2⌈ n 3 ⌉ lower bound for the area of a straight-line grid drawing of a plane 3tree with n ≥ 6 vertices, which improves the previously known lower bound ⌊ 2(n−1) 3 ⌋×⌊ 2(n−1) 3 ⌋ for plane graphs.
Computational Geometry: Theory and Applications | 2012
Rahnuma Islam Nishat; Debajyoti Mondal; Md. Saidur Rahman
A straight-line drawing of a plane graph G is a planar drawing of G, where each vertex is drawn as a point and each edge is drawn as a straight line segment. Given a set S of n points in the Euclidean plane, a point-set embedding of a plane graph G with n vertices on S is a straight-line drawing of G, where each vertex of G is mapped to a distinct point of S. The problem of deciding if G admits a point-set embedding on S is NP-complete in general and even when G is 2-connected and 2-outerplanar. In this paper, we give an O(n^2) time algorithm to decide whether a plane 3-tree admits a point-set embedding on a given set of points or not, and find an embedding if it exists. We prove an @W(nlogn) lower bound on the time complexity for finding a point-set embedding of a plane 3-tree. We then consider a variant of the problem, where we are given a plane 3-tree G with n vertices and a set S of k>n points, and present a dynamic programming algorithm to find a point-set embedding of G on S if it exists. Furthermore, we show that the point-set embeddability problem for planar partial 3-trees is also NP-complete.
graph drawing | 2013
William J. Lenhart; Giuseppe Liotta; Debajyoti Mondal; Rahnuma Islam Nishat
We prove tight bounds up to a small multiplicative or additive constant for the plane and the planar slope numbers of partial 2-trees of bounded degree. As a byproduct of our techniques, we answer a long standing question by Garg and Tamassia about the angular resolution of the planar straight-line drawings of series-parallel graphs of bounded degree.
Journal of Combinatorial Optimization | 2013
Debajyoti Mondal; Rahnuma Islam Nishat; Sudip Biswas; Md. Saidur Rahman
A convex drawing of a plane graph G is a plane drawing of G, where each vertex is drawn as a point, each edge is drawn as a straight line segment and each face is drawn as a convex polygon. A maximal segment is a drawing of a maximal set of edges that form a straight line segment. A minimum-segment convex drawing of G is a convex drawing of G where the number of maximal segments is the minimum among all possible convex drawings of G. In this paper, we present a linear-time algorithm to obtain a minimum-segment convex drawing Γ of a 3-connected cubic plane graph G of n vertices, where the drawing is not a grid drawing. We also give a linear-time algorithm to obtain a convex grid drawing of G on an
canadian conference on computer and robot vision | 2014
River Allen; Neil MacMillan; Dimitri Marinakis; Rahnuma Islam Nishat; Rayhan Rahman; Sue Whitesides
(frac{n}{2}+1)times(frac {n}{2}+1)
graph drawing | 2012
Fabrizio Frati; Marc Glisse; William J. Lenhart; Giuseppe Liotta; Tamara Mchedlidze; Rahnuma Islam Nishat
grid with at most sn+1 maximal segments, where
Journal of Discrete Algorithms | 2012
Debajyoti Mondal; Rahnuma Islam Nishat; Sue Whitesides; Md. Saidur Rahman
s_{n}=frac{n}{2}+3
Journal of Graph Algorithms and Applications | 2013
Stephane Durocher; Debajyoti Mondal; Rahnuma Islam Nishat; Sue Whitesides
is the lower bound on the number of maximal segments in a convex drawing of G.
Journal of Discrete Algorithms | 2013
Debajyoti Mondal; Rahnuma Islam Nishat; Md. Saidur Rahman; Sue Whitesides
Instrumentation of an environment with sensors can provide an effective and scalable localization solution for robots. Where GPS is not available, beacons that provide position estimates to a robot must be placed effectively in order to maximize a robots navigation accuracy and robustness. Sonar range-based beacons are reasonable candidates for low cost position estimate sensors. In this paper we explore heuristics derived from computational geometry to estimate the effectiveness of sonar beacon deployments given a predefined mobile robot path. Results from numerical simulations and experimentation demonstrate the effectiveness and scalability of our approach.
international workshop on combinatorial algorithms | 2011
Debajyoti Mondal; Rahnuma Islam Nishat; Sue Whitesides; Md. Saidur Rahman
In this paper we study bichromatic point-set embeddings of 2-colored trees on 2-colored point sets, i.e., point-set embeddings of trees (whose vertices are colored red and blue) on point sets (whose points are colored red and blue) such that each red (blue) vertex is mapped to a red (resp. blue) point. We prove that deciding whether a given 2-colored tree admits a bichromatic point-set embedding on a given convex point set is an