|
My undergrad major project work is on the topic of Visibility Polygons for Diffuse Reflections. In this model of reflection we assume that light falling on an edge of a simple polygon gets reflected in all directions. This work includes proving new bounds on the number of diffuse reflections required to flood a simple polygon fully from a point light source. It also includes designing algorithms to compute the minimum diffuse reflection path between two points. We are also working on the problem of bounding the combinatorial complexity of visibility polygons for multiple diffuse reflections. We have obtained new results for lower and upper bounds on the combinatorial complexity of diffuse reflection visibility polygons. |
|
This work is related to the computation of bounds on errors in zeros of univariate polynomials and analytic functions. Using a new and novel approach involving Rouche's theorem, we obtain very sharp error bounds. We have also generalized it to more general analytic functions, provided we can compute good bounds on a certain cyclic integral. |
|
In this work we studied ways of compressing graphs which may have applications in compressing web graphs. The particular method that we have worked on uses a theorem due to Sabidussi to convert vertex transitive graphs into Cayley graphs, which may have a short representation via the underlying abelian group. |
|
This work is a part of an Indian Space Research Organisation (ISRO) project concerning landuse and landcover classification. Here we applied ideas from Markov Random Fields and Dampster-Shafer Theory to develop new algorithms for segmentation and classification of multispectral images. As an extension of this project we have tried to use information from auxilliary sources like maps,roads,etc to increase classification accuracy and obtain Level 3 classification,as defined by the Anderson Classification scheme. |
|
Quantum Computing really fascinates me and I have been reading QC for more than 1 year now. Apart from reading the basic literature, and several papers I have been particularly interested in Quantum Random Walks and Entanglement assisted Quantum Information Processing. |
|
This study is related to various issues in randomized leader election problems. We define a notion of fairness in leader election algorithms and propose new randomized algorithms for efficient and fair leader election in a network with ring topology using randomized voting. |
|
This project is related to the factoring problem. We did a survey of known methods and figuring out problems in the current approaches that have resisted a polynomial solution. Although nothing new was discovered, I had a great time studying algebraic number theory and admiring the great works of Gauss and Lenstra. |