variable_bound set_partitioning invariant_knapsack mixed_binary general_linear

Submitter Variables Constraints Density Status Group Objective MPS File
Cézar Augusto Nascimento e Silva 4812 75395 6.26129e-04 open graphdraw 113783.5* graphdraw-opmanager.mps.gz

In the Graph Drawing problem a set of symbols must be placed in a plane and their connections routed. The objective is to produce aesthetically pleasant, easy to read diagrams. As a primary concern one usually tries to minimize edges crossing, edges’ length, waste of space and number of bents in the connections. When formulated with these constraints the problem becomes NP-Hard . In practice many additional complicating requirements can be included, such as non-uniform sizes for symbols. Thus, some heuristics such as the generalized force-direct method and Simulated Annealing have been proposed to tackle this problem. uses a grid structure to approach the Entity-Relationship (ER) drawing problem, emphasizing the differences between ER drawing and the more classical circuit drawing problems. presented different ways of producing graph layouts (e.g.: tree, orthogonal, visibility representations, hierarchic, among others) for general graphs with applications on different subjects. The ability to automatically produce high quality layouts is very important in many applications, one of these is Software Engineering: the availability of easy to understand ER diagrams, for instance, can improve the time needed for developers to master database models and increase their productivity. Our solution approach involves two phases: (\(i\)) firstly the optimal placement of entities is solved, i.e.: entities are positioned so as to minimize the distances between connected entities; and (\(ii\)) secondly, edges are routed minimizing bends and avoiding the inclusion of connectors too close. We present the model for the first phase of our problem.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 4812 4812
Constraints 75395 75395
Binaries 4512 4512
Integers 96 96
Continuous 204 204
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.000626129 0.000626129
Nonzeroes 227160 227160
Constraint Classification Properties
Original Presolved
Total 75395 75395
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 0 0
Variable Bound 246 246
Set Partitioning 1128 1128
Set Packing 0 0
Set Covering 0 0
Cardinality 0 0
Invariant Knapsack 69184 69184
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 0
Integer Knapsack 0 0
Mixed Binary 109 109
General Linear 4728 4728
Indicator 0 0


Available nonzero structure and decomposition information. Further information can be found here.

value min median mean max
Components 0.4771212
Constraint % 49.0165 49.0165 49.0165 49.0165
Variable % 49.0025 49.0025 49.0025 49.0025
Score 0.4999440

Best Known Solution(s)

Find solutions below. Download the archive containing all solutions from the Download page.

ID Objective Exact Int. Viol Cons. Viol Obj. Viol Submitter Date Description
2 113783.5 0 0 0 Robert Ashford and Alkis Vazacopoulus 2019-12-18 Found using ODH|CPlex
1 144690.5 0 0 0 - 2018-10-13 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to graphdraw-opmanager in the collection. This similarity analysis is based on 100 scaled instance features describing properties of the variables, objective function, bounds, constraints, and right hand sides.

Instance Status Variables Binaries Integers Continuous Constraints Nonz. Submitter Group Objective Tags
graphdraw-grafo2 open 9258 8844 134 280 203455 612366 Cézar Augusto Nascimento e Silva graphdraw 95024.5* variable_bound set_partitioning invariant_knapsack mixed_binary general_linear
graphdraw-mainerd open 2050 1860 62 128 20661 62350 Cézar Augusto Nascimento e Silva graphdraw 49016* variable_bound set_partitioning invariant_knapsack mixed_binary general_linear
neos-3402294-bobin easy 2904 2616 0 288 591076 2034890 Jeff Linderoth neos-pseudoapplication-71 0.0672499999999995 benchmark benchmark_suitable precedence set_partitioning set_covering invariant_knapsack mixed_binary
graphdraw-domain easy 254 180 20 54 865 2600 Cézar Augusto Nascimento e Silva graphdraw 19686 benchmark benchmark_suitable variable_bound set_partitioning invariant_knapsack mixed_binary general_linear
graphdraw-gemcutter easy 166 112 16 38 474 1420 Cézar Augusto Nascimento e Silva graphdraw 7118.5 benchmark_suitable variable_bound set_partitioning invariant_knapsack mixed_binary general_linear


title = {Drawing graphs with mathematical programming and variable neighborhood search},
journal = {Electronic Notes in Discrete Mathematics},
volume = {58},
pages = {207--214},
year = {2017},
issn = {1571-0653},
doi = {},
author = {Cézar Augusto N. e Silva and Haroldo Gambini Santos}

Last Update Feb 11, 2020 by Gabriel Kressin
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