In our current approach we employ a greedy strategy tackle the re-coloring problem defined in Section 4.1. The major reasons for utilizing a greedy strategy is, as in other many approaches based on some greedy algorithms, we believe that it is useful as well as crucial for handling real world data, especially for large scale data. Based on this hypothesis, both the selection of vertex to be re-colored and the selection of the color to be assigned, is conducted in greedy fashion. The other side of our greedy algorithm is that, besides it tries to improve the quality of partition while satisfying the constraints, there can still be better solutions for the re-coloring problem. If finding out better solutions is the most important (and, the only) interest, then, it would be possible to seek other much more expensive approaches. For instance, it might be possible to incorporate some kind of back-tracking for the re-coloring of the vertices. Such a recursive approach might be useful, both for the conceptual simplicity of the algorithm as well as the quality of the obtained solutions, in compensation for the incurred computational complexity. In addition, there are many interesting issues to pursue: 1. more experiments and comparison for our algorithm on real world datasets, and 2. extension of our re-coloring approach for the critical vertices As for (1), medical datasets or large scale image datasets seem interesting. As for (2), relaxing the constraints on the critical vertices seems promising for finding out better partition.