# We use Barry Center crossing reduction heuristics. This is a two layer crossing reduction process.

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We use Barry Center crossing reduction heuristics. This is a two layer crossing reduction process. It is applied from top to bottom layer then bottom to top, this completes one iteration.
Assign artificial positions to first layer and calculate barry center weights of nodes at second layer. Reorder the nodes at second layer in ascending order of their barycenter weights. The above equation is for top-down sweeps of the layered graph. Similarly use Successors of v in bottom-up sweeps in the above equation. This process might not remove all edge crossings but gives a good starting point for further Subgraph Crossing Reduction process.
4.2 Subgraph Crossing Reduction
Global crossing reduction reduces some crossings but can reorder the nodes
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A topological traversal of subgraph ordering graph gives ordering αo denoting which subgraph is left of other subgraph.
5. POSITIONING
The edge crossings are reduced and nodes are placed according to their subgraphs at each layer. Now we need to calculate absolute positions for graph nodes such that there will be enough space to draw subgraph boundaries. To draw subgraph vertical boundaries straight we add trail of dummy vertical nodes one to the left and one to the right side of each layer in every subgraph.
The goal is to position the long edges as straight as possible and vertical borders of subgraph strictly vertical without reordering the nodes at any layer. We present a heuristic approach based on Brandes[] approach. The nodes have different height and width. There should be no overlap between any two nodes and node and subgraph boundary. The process consists of three steps. The first and second steps are carried out four times. The first algorithm referred as vertical alignment, to align nodes with its either median upper or median lower neighbor node. This will give maximum possible straight long edges positions in upward and downward direction. The alignment conflicts are resolved with leftmost and rightmost direction. Combination of the directions creates four alignments namely Upward-Left, Upward-Right, Downward-Left and Downward-Right. In second step each alignment is given absolute positions according to four alignments. In last step these alignments