My current research encompasses the design of approximation algorithms for the so called ``art gallery problem(s)'' in computational geometry for computing vertex, edge and interior point guard sets for guarding two dimensional art galleries, modelled as polygons.
Euclidean shortest paths, link paths and reflection paths between points inside polygons provide local information about the shape of the entire polygonal region. The focus of research in this context is to characterize shape and combinatorial properties of polygonal regions in terms of properties of such paths.
I am also working on estimating bounds on the sizes of separating and bisecting families for set systems (hypergraphs).
Induced-bisecting families of bicolorings for hypergraphs by Balachandran N., Mathew R. , Mishra T. K., Pal S. P. Discrete Mathematics 341 1732-1739 (2018)
Constant Approximation Algorithms for Guarding Simple Polygons using Vertex Guards by Bhattacharya P., Ghosh S. K., Pal S. P. - (2018)
System of unbiased representatives for a collection of bicolorings by Balachandran N., Mathew R. , Mishra T. K., Pal S. P. - (2017)
Bisecting and D-secting families for set systems by Balachandran N., Mathew R. , Mishra T. K., Pal S. P. Discrete Applied Mathematics - (Accepted/In-Press)
Visibility with multiple reflections by B. Aronov, A. Davis, T. K. Dey, S. P. Pal and D. Chithra Prasad Discrete and Computational Geometry vol. 20, Springer-Verlag 61-78 (1988)
Visibility with one reflection by B. Aronov, A. Davis, T. K. Dey, S. P. Pal and D. Chithra Prasad Discrete and Computational Geometry vol 19, Springer-Verlag 553-574 (1998)
A combinatorial approach for studying LOCC transformations of multipartite states by Sudhir Kumar Singh (M. Sc. Mathematics and Computing 1999-2004), S. P. Pal, Somesh Kumar (Dept. of Mathematics, IIT Kharagpur), and R. Srikanth Journal of Mathematical Physics 46, 122105, AIP - (2005)
Diffuse Reflection Diameter and Radius for Convex-Quadrilateralizable Polygons Elsevier by Arindam Khan, Sudebkumar Prasant Pal, Mridul Aanjaneya, Arijit Bishnu, Subhas C. Nandy Discrete Applied Mathematics 161(10-11), Elsevier 1496-1505 (2013)
Maximum weighted independent sets with a budget by Kalra T., Mathew R. , Pal S. P., Pandey V. CALDAM 2017 254-266 (2017)
Computing the shortest path tree in a weak visibility polygon by S. K. Ghosh, A. Maheshwari, S. P. Pal, S. Saluja and C. E. Veni Madhavan Proceedings of the eleventh conference on Foundations of Software Technology and Theoretical Computer Science, New Delhi, India, Lecture Notes in Computer Science, Springer-Verlag vol. 560, Springer-Verlag 369-389 (1991)
Area of Research: Computational geometry