Geometry, flows, and graph-partitioning algorithms

Graph partitioning is a computational problems to divide the vertices of a graph into two large pieces with minimum number of the edges. The application of partitioning can be used for computer vision, data analysis, image segmentation, and image analysis. The geometric approach of partitioning start with drawing the graph in a geometric space by keeping small distance between its endpoint and points are spread out. The graph need to draw in a way that the sum of squares of the length of the edges is small and square of the distance between the average pair of points is a fixed constant. Geometric approach can determine how much distortion is require to map the metric space into a Euclidean metric space. Flow based approach also can be used for graph partitioning and designing fast algorithms.