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Tim Dwyer, Yehuda Koren, Kim Marriott, "Drawing Directed Graphs Using Quadratic Programming," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 4, pp. 536548, July/August, 2006.  
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@article{ 10.1109/TVCG.2006.67, author = {Tim Dwyer and Yehuda Koren and Kim Marriott}, title = {Drawing Directed Graphs Using Quadratic Programming}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {12}, number = {4}, issn = {10772626}, year = {2006}, pages = {536548}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2006.67}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Drawing Directed Graphs Using Quadratic Programming IS  4 SN  10772626 SP536 EP548 EPD  536548 A1  Tim Dwyer, A1  Yehuda Koren, A1  Kim Marriott, PY  2006 KW  Directed graphs KW  graph drawing KW  hierarchy KW  force directed algorithms KW  majorization KW  quadratic programming. VL  12 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—We describe a new method for visualization of directed graphs. The method combines constraint programming techniques with a high performance forcedirected placement (FDP) algorithm. The resulting placements highlight hierarchy in directed graphs while retaining useful properties of FDP; such as emphasis of symmetries and preservation of proximity relations. Our algorithm automatically identifies those parts of the digraph that contain hierarchical information and draws them accordingly. Additionally, those parts that do not contain hierarchy are drawn at the same quality expected from a nonhierarchical, undirected layout algorithm. Our experiments show that this new approach is better able to convey the structure of large digraphs than the most widely used hierarchical graphdrawing method. An interesting application of our algorithm is
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