Papers by Dr. Sukumar Mondal
Optimal Sequential And Parallel Algorithms To Compute A Steiner Tree On Permutation Graphs
International Journal of Computer Mathematics, Aug 1, 2003
This paper presents an optimal sequential and an optimal parallel algorithm to compute a minimum ... more This paper presents an optimal sequential and an optimal parallel algorithm to compute a minimum cardinality Steiner set and a Steiner tree. The sequential algorithm takes O ( n ) time and parallel algorithm takes O (log n ) time and O ( n /log n ) processors on an EREW PRAM model.
Domination and competition have been there since the beginning of the Universe. Bigger stars domi... more Domination and competition have been there since the beginning of the Universe. Bigger stars dominate the smaller ones and draw them towards themselves. Domination and competition are such phenomenon which nothing in this universe can stay without. Stronger things and animals dominate the weaker ones. Again, when there are more than one strong dominant, there comes competition among them. To measure domination and competition together, we introduce here a domination competition graph, through which we identify the most competitive and dominating variables. By dominating competition number, we calculate which nodes (when we draw a graph corresponding perception) are more powerful and how much powerful. We have used forest biodiversity network as an example here. In the end, an application of domination competitions to e-commerce industry is illustrated.
Breast DCE-MRI segmentation for lesion detection using Chimp Optimization Algorithm
Expert Systems with Applications
Edge-vertex domination on interval graphs
Discrete Mathematics, Algorithms and Applications
For an undirected as well as connected graph [Formula: see text], a node point [Formula: see text... more For an undirected as well as connected graph [Formula: see text], a node point [Formula: see text] is edge-vertex dominated by an edge [Formula: see text] if [Formula: see text] is incident to [Formula: see text] or [Formula: see text] is incident to an adjacent edge of [Formula: see text]. A set [Formula: see text] is called an edge-vertex dominating set of [Formula: see text] if every node point of [Formula: see text] is edge-vertex dominated by at least one edge of [Formula: see text]. The minimum cardinality among all edge-vertex dominating sets is the edge-vertex domination number, symbolled by [Formula: see text]. Here, we propose an algorithm that runs in [Formula: see text]-time for determining a minimum-cardinality [Formula: see text] of interval graph with [Formula: see text] nodes. We also study some properties relating to the edge-vertex dominating set of interval graphs.
Magnetic Resonance Image of Breast Segmentation by Multi-Level Thresholding Using Moth-Flame Optimization and Whale Optimization Algorithms
Pattern Recognition and Image Analysis, 2022
Abstract In this paper, we propose two breast lesion segmentation methods in dynamic contrast enh... more Abstract In this paper, we propose two breast lesion segmentation methods in dynamic contrast enhanced magnetic resonance image (DCE-MRI) using moth-flame optimizer (MFO) and whale optimization algorithm (WOA). In the first method, at the outset, MR images are denoised using the median filter in the preprocessing step. After that, a multi-level thresholding technique using MFO is used to search the suitable thresholds through entropy maximization to segment the lesions in MR images. In the second method, WOA is used in place of MFO in the framework of the first method. Segment the breast DCE-MRI lesion detection using MFO and WOA. The proposed methods are applied to 50 Sagittal T2-weighted DCE-MRI slices of 10 patients. The proposed methods are compared with algorithms such as particle swarm optimizer (PSO), improved Markov random field (IMRF), hidden Markov random field (HMRF), and conventional Markov random field (CMRF) methods. The high accuracy level of 99 . 88% and sensitivity 95 . 51% are achieved using the proposed MFO segmentation method. The high accuracy and sensitivity level of another proposed method WOA are achieved, 99 . 78 and 93 . 09%, respectively. The experimental results demonstrate that the proposed methods perform better than other methods in breast lesion segmentation in DCE-MRI.
WSEAS Transactions on Computer Research, Jul 6, 2021
Software developers have been presented with so many tools meant to assist then during the develo... more Software developers have been presented with so many tools meant to assist then during the development process. Tools like autocomplete, intelli-sense, linters, and other static analysis solutions. All such tools have one underlying goal, to promote productivity and improve quality. Much research has been conducted on the topic of software quality and its direct benefits both during and after the development cycle. Various methods of measuring and improving quality in software products have been implemented at a grand scale. However, software developers are still left with the choice of implementation details. One such detail is the choice of identifier names in the code written. Few publications have focused on conventions, guides, or best-practices on the topic of identifiers naming choices (not to be confused with coding styles). Much time and energy is misused by developers while choosing an appropriate identifier name, as well as by other developers later on when trying to understand the choice made by their colleagues. By aggregating and compiling a list of readily available identifier names that developers can choose from, will allow them to focus on other keys aspects of development.
A sequential and parallel algorithm for disjoint cliques problem on interval graphs
Using DAG approach,A sequential algorithm is presented to solve disjoint cliques problem on inter... more Using DAG approach,A sequential algorithm is presented to solve disjoint cliques problem on interval graph G which takes O(n^2) time where n is the number of vertices of the graph. For the same problem a O(log2n) time parallel algorithm is presented which takes processors on an EREW PRAM model. Also, on a CREW model it takes O(logn) time with O(n^(3+e) ),e>0 processors.
Breast Lesion Segmentation in DCE-MRI using Multi-Objective Clustering with NSGA-II
2022 International Conference on Innovative Trends in Information Technology (ICITIIT)
Breast cancer causes the highest death among all types of cancers in women. Early detection and d... more Breast cancer causes the highest death among all types of cancers in women. Early detection and diagnosis leading to early treatment can save the life. The computer-assisted methodologies for breast dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) segmentation can help the radiologists/doctors in the diagnosis of the disease as well as further treatment planning. In this article, we propose a breast DCE-MRI segmentation method using a hard-clustering technique with a Non-dominated Sorting Genetic Algorithm (NSGA-II). The well-known cluster validity metrics namely DB-index and Dunn-index are utilized as objective functions in NSGA-II algorithm. The noise and intensity inhomogeneities in MRI are removed from MRI in the preprocessing step as these artifacts affect the segmentation process. After segmentation, the lesions are separated and finally, localized in the MRI. The devised method is applied to segment 10 Sagittal T2-Weighted fat-suppressed DCE-MRI of the breast. A comparative study has been conducted with the K-means algorithm and the devised method outperforms K-means both quantitatively and qualitatively.
Energy of interval-valued fuzzy graphs and its application in ecological systems
Journal of Applied Mathematics and Computing, 2021
International Journal of Innovative Technology and Exploring Engineering, 2021
For cancer detection and tissue characterization, DCE-MRI segmentation and lesion detection is a ... more For cancer detection and tissue characterization, DCE-MRI segmentation and lesion detection is a critical image analysis task. To segment breast MR images for lesion detection, a hard-clustering technique with Grammatical Fireworks algorithm (GFWA) is proposed in this paper. GFWA is a Swarm Programming (SP) system for automatically generating computer programs in any language. GFWA is used to create the cluster core for clustering the breast MR images in this article. The presence of noise and intensity inhomogeneities in MR images complicates the segmentation process. As a result, the MR images are denoised at the start, and strength inhomogeneities are corrected in the preprocessing stage. The proposed GFWA-based clustering technique is used to segment the preprocessed MR images. Finally, from the segmented images, the lesions are removed. The proposed approach is tested on 5 patients’ 25 DCE-MRI slices. The proposed method’s experimental findings are compared to those of the Gram...
The average distance () G µ of a finite graph = (,) G V E is the average of the distances over al... more The average distance () G µ of a finite graph = (,) G V E is the average of the distances over all unordered pairs of vertices. A minimum average distance spanning tree of G is a spanning tree of G with minimum average distance. Such a tree is sometimes referred to as a minimum routing cost spanning tree. In this paper, we present an efficient algorithm to compute a minimum average distance spanning tree on permutation graphs in 2 () O n time, where n is the number of vertices of the graph.
International Journal of Computer Mathematics, 2002
Let G (V, E) be a simple graph and k be a ®xed positive integer. A vertex w is said to be a kneig... more Let G (V, E) be a simple graph and k be a ®xed positive integer. A vertex w is said to be a kneighbourhood-cover of an edge (u, v) if d(u, w) k and d(v, w) k. A set C V is called a kneighbourhood-covering set if every edge in E is k-neighbourhood-covered by some vertices of C. This problem is NP-complete for general graphs even it remains NP-complete for chordal graphs. Using dynamic programming technique, an O(n) time algorithm is designed to solve minimum 2-neighbourhood-covering problem on interval graphs. A data structure called interval tree is used to solve this problem.
The average distance () G µ of a finite graph = (,) G V E is the average of the distances over al... more The average distance () G µ of a finite graph = (,) G V E is the average of the distances over all unordered pairs of vertices. A minimum average distance spanning tree of G is a spanning tree of G with minimum average distance. Such a tree is sometimes referred to as a minimum routing cost spanning tree. In this paper, we present an efficient algorithm to compute a minimum average distance spanning tree on permutation graphs in 2 () O n time, where n is the number of vertices of the graph.
Computation of inverse 1-centre location problem on the weighted interval graphs
Int. J. Comput. Sci. Math., 2017
Let TIG be the tree corresponding to the weighted interval graph G = (V, E). In an inverse 1-cent... more Let TIG be the tree corresponding to the weighted interval graph G = (V, E). In an inverse 1-centre location problem the parameter of an interval tree TIG corresponding to the weighted interval graph G = (V, E), like vertex weights have to be modified at minimum total cost such that a pre-specified vertex s ∈ V becomes the 1-centre of the interval graph G. In this paper, we present an O(n) time algorithm to find an inverse 1-centre location problem on the weighted tree TIG corresponding to the weighted interval graph, where the vertex weights can be changed within certain bounds and n is the number of vertices of the graph G.
ArXiv, 2014
In a graph G , a spanning tree T is said to be a tree t-spanner of the graph G if the distance be... more In a graph G , a spanning tree T is said to be a tree t-spanner of the graph G if the distance between any two vertices in T is at most t times their distance in G. The tree t-spanner has many applications in networks an d distributed environments. In this paper, an algorithm is presented to find a tree 3 -spanner on trapezoid graphs in ) ( 2 n O time, where n is the number of vertices of the graph.
Computation of Inverse 1-Center Location Problem on the Weighted Trees
Let T be a tree with (1)n vertices and n edges with positive edge weights. The inverse 1-center p... more Let T be a tree with (1)n vertices and n edges with positive edge weights. The inverse 1-center problem on an edge weighted tree consists in changing edge weights at minimum cost so that a pre-specified vertex becomes the 1-center. In the context of location problems Cai et al. [9] proved that the inverse 1-center location problem with edge length modification on general un-weighted directed graphs is NP-hard, while the underlying center location problem is solvable in polynomial time. Alizadeh et al. [1] have designed an algorithm for inverse 1-center location problem with edge length augmentation on trees in (log)Onn time, using a set of suitably extended AVL-search trees. In [2], Alizadeh et al. have designed a combinatorial algorithm for inverse absolute on trees in 2()On time when topology not allowed and 2()Onr time when topology allowed. In this paper, we present an optimal algorithm to find an inverse 1-center location on the weighted trees with (1)n vertices and n edges, wh...
Finding cliques and clique covers in graphs are one of the most needful tasks. In this paper, int... more Finding cliques and clique covers in graphs are one of the most needful tasks. In this paper, interval-valued fuzzy cliques (IVFQs) and interval-valued fuzzy clique covers (IVFQCs) of an interval-valued fuzzy graph (IVFG) are introduced by introducing the fuzziness because, the crisp graphs has some limitations in real world due to uncertainty of vagueness. Here, the concept of cliques and clique covers are slightly modified so that every IVFQ is complete. Also, a clique cover of a crisp graph always covers all the edges and vertices of the graph whereas, the IVFQCs obtained by fuzzify to the clique covers does not satisfy the property. Hence, the definition is modified and studied some theorems on it. To better understand the useability of this work a model application is stated in this paper.
Minimum r-neighborhood covering set of permutation graphs
Discrete Mathematics, Algorithms and Applications, 2021
For a connected graph G(V,E) and a fixed integer r > 0, a node q ∈ V r-dominates another node ... more For a connected graph G(V,E) and a fixed integer r > 0, a node q ∈ V r-dominates another node s ∈ V if d(q,s) ≤ r. An edge (q,s) is r-neighborhood covered by a vertex t, if d(q,t) ≤ r and d(s,t) ≤ ...
Theory and Applications of Mathematical Science Vol. 2
This book covers all areas of mathematical science. The contributions by the authors include nonl... more This book covers all areas of mathematical science. The contributions by the authors include nonlinear integral equation; Darbo's fixed point theorem; Weibull parameters; MATLAB; trapezoid graphs; fixed point; common fixed point; fuzzy cone metric space; Dirichlet problem; Quadrature surfaces; agent-based modelling; nonlinear dynamics; topological groups; free topological groups; nonconsistency of the conservation laws equations; degenerate transformation; discrete solutions; meromorphic functions; Pad-approximants; (p, q)-order and (p, q)-type; logarithmic capacity; quasinearly subharmonic; families of quasinearly subharmonic functions etc. This book contains various materials suitable for students, researchers and academicians in the field of mathematical science.
Social Network Analysis and Mining
In this study, cluster hypergraphs are introduced to generalize the concept of hypergraphs, where... more In this study, cluster hypergraphs are introduced to generalize the concept of hypergraphs, where cluster nodes are allowed. Few related terms and properties on cluster hypergraphs are discussed. Some operations, including the Cartesian product, union, intersection, etc., are studied. Different types of matrix representations and isomorphism are also proposed on cluster hypergraphs. The notion of an effective degree for nodes is introduced to capture the group/ cluster effects. At last, the area of applications and future directions with conclusions is deployed.
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Papers by Dr. Sukumar Mondal