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 166 474 1.80469e-02 easy graphdraw 7118.5 graphdraw-gemcutter.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 166 166
Constraints 474 474
Binaries 112 112
Integers 16 16
Continuous 38 38
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.0180469 0.0180469
Nonzeroes 1420 1420
Constraint Classification Properties
Original Presolved
Total 474 474
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 0 0
Variable Bound 43 43
Set Partitioning 28 28
Set Packing 0 0
Set Covering 0 0
Cardinality 0 0
Invariant Knapsack 224 224
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 0
Integer Knapsack 0 0
Mixed Binary 23 23
General Linear 156 156
Indicator 0 0


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

value min median mean max
Components 0.4771212
Constraint % 40.0844 40.0844 40.0844 40.0844
Variable % 45.1807 45.1807 45.1807 45.1807
Score 0.4394790

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 7118.5 7118.5 0 0 0 - 2018-10-13 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to graphdraw-gemcutter 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-domain easy 254 180 20 54 865 2600 Cézar Augusto Nascimento e Silva graphdraw 19685.99997550038 benchmark 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
neos-3696678-lyvia easy 7683 7516 167 0 9004 30452 Jeff Linderoth neos-pseudoapplication-56 83.74999995899876 decomposition variable_bound set_covering cardinality invariant_knapsack mixed_binary general_linear
neos-3009394-lami open 2757 2704 52 1 2028 6760 Jeff Linderoth neos-pseudoapplication-90 5.5* set_partitioning 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}

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