benchmark benchmark_suitable variable_bound set_partitioning invariant_knapsack mixed_binary general_linear

Submitter Variables Constraints Density Status Group Objective MPS File
Cézar Augusto Nascimento e Silva 254 865 1.18338e-02 easy graphdraw 19685.99997550038 graphdraw-domain.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 254 254
Constraints 865 865
Binaries 180 180
Integers 20 20
Continuous 54 54
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.0118338 0.0118338
Nonzeroes 2600 2600
Constraint Classification Properties
Original Presolved
Total 865 865
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 0 0
Variable Bound 57 57
Set Partitioning 45 45
Set Packing 0 0
Set Covering 0 0
Cardinality 0 0
Invariant Knapsack 480 480
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 0
Integer Knapsack 0 0
Mixed Binary 35 35
General Linear 248 248
Indicator 0 0


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

value min median mean max
Components 0.4771212
Constraint % 42.0809 42.0809 42.0809 42.0809
Variable % 46.0630 46.0630 46.0630 46.0630
Score 0.4539440

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
1 19686 19686 6e-07 1e-07 0 - 2018-10-13 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to graphdraw-domain 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-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
graphdraw-mainerd open 2050 1860 62 128 20661 62350 Cézar Augusto Nascimento e Silva graphdraw 39852.99999999995* variable_bound set_partitioning invariant_knapsack mixed_binary general_linear
graphdraw-opmanager open 4812 4512 96 204 75395 227160 Cézar Augusto Nascimento e Silva graphdraw 103535.4999999998* variable_bound set_partitioning invariant_knapsack mixed_binary general_linear
graphdraw-grafo2 open 9258 8844 134 280 203455 612366 Cézar Augusto Nascimento e Silva graphdraw 72118.5* variable_bound set_partitioning invariant_knapsack mixed_binary general_linear
neos-932721 easy 22266 21825 0 441 18085 107908 NEOS Server Submission neos-pseudoapplication-56 52030 decomposition precedence variable_bound set_packing invariant_knapsack mixed_binary


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 Dec 06, 2022 by Jan Krüger
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