I am working on designing new sequential and parallel algorithms, and improving existing ones, to solve various computational problems such as: graph isomorphism, membership in permutation groups (generalized Rubik's Cube), network flow, matching in graphs, Boolean matrix multiplication, and connectivity of graphs.
Recently, I have been concentrating on the following problems.
Dynamic graph algorithms. These are algorithms which solve problems in which the input graph keeps changing; e.g. edges are inserted and deleted or weights are increased or decreased. The goal is to maintain the solution in such a way that the changes in it can be found faster than resolving the problem from scratch.
String processing algorithms with applications to molecular biology. There exist computational problems associated with the human genome project where algorithmic improvements are possible. An area were considerable progress has already been achieved is the speed up of various dynamic programming techniques.