I am interested in problem-solving in general, more specifically in problems which we can model them with graphs. The fields that currently I work on them are as follows. If you are interested in any of them and you want to know more about my researches, just drop me an email.
Disjoint Paths Problem: I am interested in different variations of this problem. Most of the theoretical algorithms for the disjoint paths problem are in special classes of digraphs and even there they are impractical. I would like to narrow the gap between theory and practice. Together with my coauthors, I considered directed disjoint paths and its variations such as disjoint paths with congestions, rerouting paths etc. In near future we will do more on this topic. These are our results up to now:
Dominating Sets Problem in the Local/Congest model: In the Local Model of computation, every node of a graph can be seen as a Turing machine. Nodes can communicate to their neighborhood in each round. We aim to obtain a dominating set of a graph which is a good approximation to the optimum dominating sets, this we did up to now for some classes of graphs. I do not know how far we can go! The following is the list of our related works on this topic:
- Erdős-Pósa Property for Directed Graphs: We recently provide a full classification for the class of strongly connected digraphs, we would like to provide a full characterization for vertex cyclic digraphs. Our latest result on this topic is the following: