Large volumes of structured and semi-structured data are being generated every day. Processing this large amount of data and extracting important information is a challenging task. The goal of an automatic text summarization is to preserve the key information and the overall meaning of the article to be summarized. In this paper, a graph-based approach is followed to generate an extractive summary, where sentences of the article are considered as vertices, and weighted edges are introduced based on the cosine similarities among the vertices. A possible subset of maximal independent sets of vertices of the graph is identified with the assumption that adjacent vertices provide sentences with similar information. The degree centrality and clustering coefficient of the vertices are used to compute the score of each of the maximal independent sets. The set with the highest score provides the final summary of the article. The proposed method is evaluated using the benchmark BBC News data to demonstrate its effectiveness and is applied to the COVID-19 Twitter data to express its applicability in topic modeling. Both the application and comparative study with other methods illustrate the efficacy of the proposed methodology.

This article presents a combinatorial algorithm to find a shortest triangular path (STP) between two points inside a digital object imposed on triangular grid that runs in [Formula: see text] time, where n is the number of pixels on the contour of the object and g is the grid size. Initially, the inner triangular cover which maximally inscribes the object is constructed to ensure that the path lies within the object. An appropriate bounding parallelogram is considered with those two points in diagonally opposite corners and then one of the semi-perimeters of the parallelogram is traversed. Certain combinatorial rules are formulated based on the properties of triangular grid and are applied during the traversal whenever required to shorten the triangular path. A shortest triangular path between any two points may not be unique. Another combinatorial algorithm is presented, which finds the family of shortest triangular path (FSTP) (i.e., the region containing all possible shortest triangular paths) between two given points inside a digital object and runs in [Formula: see text] time. Experimental results are presented to verify the correctness, robustness, and efficacy of the algorithms. STP and FSTP can be useful for shape analysis of digital objects and determining shape signatures. 1

This article presents a combinatorial algorithm to find a shortest triangular path (STP) between two points inside a digital object imposed on triangular grid that runs in O(nglogng)time, where n is the number of pixels on the contour of the object and g is the grid size. Initially, the inner triangular cover which maximally inscribes the object is constructed to ensure that the path lies within the object. An appropriate bounding parallelogram is considered with those two points in diagonally opposite corners and then one of the semi-perimeters of the parallelogram is traversed. Certain combinatorial rules are formulated based on the properties of triangular grid and are applied during the traversal whenever required to shorten the triangular path. A shortest triangular path between any two points may not be unique. Another combinatorial algorithm is presented, which finds the family of shortest triangular path (FSTP) (i.e., the region containing all possible shortest triangular paths) between two given points inside a digital object and runs in O(nglogng) time. Experimental results are presented to verify the correctness, robustness, and efficacy of the algorithms. STP and FSTP can be useful for shape analysis of digital objects and determining shape signatures.