|  | 1 | = Benchmark data for the minimum-cost flow problem = | 
                          |  | 2 |  | 
                          |  | 3 | This page provides a benchmark data suite for the minimum-cost network flow problem. | 
                          |  | 4 |  | 
                          |  | 5 | Most networks were generated with standard random generators: | 
                          |  | 6 | [ftp://dimacs.rutgers.edu/pub/netflow/generators/network/netgen/ NETGEN], | 
                          |  | 7 | [ftp://dimacs.rutgers.edu/pub/netflow/generators/network/gridgen/ GRIDGEN], | 
                          |  | 8 | [ftp://dimacs.rutgers.edu/pub/netflow/generators/network/grid-on-torus/ GOTO], and | 
                          |  | 9 | [ftp://dimacs.rutgers.edu/pub/netflow/generators/network/gridgraph/ GRIDGRAPH], | 
                          |  | 10 | which are available at the [ftp://dimacs.rutgers.edu/pub/netflow/ FTP site] | 
                          |  | 11 | of the [http://dimacs.rutgers.edu/Challenges/ 1st DIMACS Implementation Challenge] (1990-1991). | 
                          |  | 12 | Other instances were generated based on either real-life | 
                          |  | 13 | road networks or maximum flow problems arising in computer vision applications. | 
                          |  | 14 |  | 
                          |  | 15 | All instances are given in [http://lpsolve.sourceforge.net/5.5/DIMACS_mcf.htm DIMACS format] | 
                          |  | 16 | and contain only integer data. | 
                          |  | 17 |  | 
                          |  | 18 |  | 
                          |  | 19 | == NETGEN instances == | 
                          |  | 20 | These networks were generated with [ftp://dimacs.rutgers.edu/pub/netflow/generators/network/netgen/ NETGEN]. | 
                          |  | 21 |  | 
                          |  | 22 | '''Parameters:''' | 
                          |  | 23 |  | 
                          |  | 24 | '''Download:''' [http://lime.cs.elte.hu/~kpeter/data/mcf/netgen/] | 
                          |  | 25 |  | 
                          |  | 26 |  | 
                          |  | 27 | == GRIDGEN instances == | 
                          |  | 28 | These networks were generated with [ftp://dimacs.rutgers.edu/pub/netflow/generators/network/gridgen/ GRIDGEN]. | 
                          |  | 29 |  | 
                          |  | 30 | '''Parameters:''' | 
                          |  | 31 |  | 
                          |  | 32 | '''Download:''' [http://lime.cs.elte.hu/~kpeter/data/mcf/gridgen/] | 
                          |  | 33 |  | 
                          |  | 34 |  | 
                          |  | 35 | == GOTO instances == | 
                          |  | 36 | These networks were generated with [ftp://dimacs.rutgers.edu/pub/netflow/generators/network/grid-on-torus/ GOTO] (Grid On Torus). | 
                          |  | 37 |  | 
                          |  | 38 | '''Parameters:''' | 
                          |  | 39 |  | 
                          |  | 40 | '''Download:''' [http://lime.cs.elte.hu/~kpeter/data/mcf/goto/] | 
                          |  | 41 |  | 
                          |  | 42 | == GRIDGRAPH instances == | 
                          |  | 43 | These networks were generated with [ftp://dimacs.rutgers.edu/pub/netflow/generators/network/gridgraph/ GRIDGRAPH]. | 
                          |  | 44 |  | 
                          |  | 45 | '''Parameters:''' | 
                          |  | 46 |  | 
                          |  | 47 | '''Download:''' [http://lime.cs.elte.hu/~kpeter/data/mcf/gridgraph/] | 
                          |  | 48 |  | 
                          |  | 49 |  | 
                          |  | 50 | == ROAD instances == | 
                          |  | 51 | These instances were generated based on real-life road networks. | 
                          |  | 52 | We used the TIGER/Line data files of several states of the USA, | 
                          |  | 53 | which are available at the [http://www.dis.uniroma1.it/~challenge9/ web site] | 
                          |  | 54 | of the [http://dimacs.rutgers.edu/Challenges/ 9th DIMACS Implementation Challenge] (2005-2006): | 
                          |  | 55 | [http://www.dis.uniroma1.it/challenge9/data/tiger/]. | 
                          |  | 56 |  | 
                          |  | 57 | The cost of an arc is set to the travel time on the corresponding road section. | 
                          |  | 58 | The number of supply and demand nodes are both set to ''sqrt''(''n'')/10 | 
                          |  | 59 | (where ''sqrt''(''n'') denotes the square root of the number of nodes in the network). | 
                          |  | 60 | These nodes are selected randomly, and the supply-demand values are determined | 
                          |  | 61 | by a maximum flow computation. | 
                          |  | 62 |  | 
                          |  | 63 | * ''ROAD-PATHS family.'' | 
                          |  | 64 | The arc capacities are uniformly set to one. | 
                          |  | 65 | * ''ROAD-FLOW family.'' | 
                          |  | 66 | The capacity of an arc is set 40, 60, 80, or 100 according to the road category. | 
                          |  | 67 |  | 
                          |  | 68 | '''Download:''' [http://lime.cs.elte.hu/~kpeter/data/mcf/road/] | 
                          |  | 69 |  | 
                          |  | 70 |  | 
                          |  | 71 | == VISION instances == | 
                          |  | 72 | These instances were generated based on large-scale | 
                          |  | 73 | maximum flow problems arising in computer vision applications. | 
                          |  | 74 | The original maximum flow problem instances were made available by the | 
                          |  | 75 | [http://vision.csd.uwo.ca/ Computer Vision Research Group] at the | 
                          |  | 76 | [http://www.csd.uwo.ca/ University of Western Ontario]. | 
                          |  | 77 | They can be accessed at [http://vision.csd.uwo.ca/data/maxflow/]. | 
                          |  | 78 |  | 
                          |  | 79 | We used some of the segmentation instances related to medical image analysis, | 
                          |  | 80 | which are defined on 3D grids (the `bone_sub*_n6c100` files). | 
                          |  | 81 | These networks were converted to minimum-cost maximum flow problem instances | 
                          |  | 82 | applying different arc cost functions. | 
                          |  | 83 |  | 
                          |  | 84 | * ''VISION-RND family.'' | 
                          |  | 85 | The arc costs are selected uniformly at random. | 
                          |  | 86 | * ''VISION-PROP family.'' | 
                          |  | 87 | The cost of an arc is approximately proportional to its capacity. | 
                          |  | 88 | * ''VISION-INV family.'' | 
                          |  | 89 | The cost of an arc is approximately inversely proportional to its capacity. | 
                          |  | 90 |  | 
                          |  | 91 | '''Download:''' [http://lime.cs.elte.hu/~kpeter/data/mcf/vision/] |