variable_bound set_partitioning invariant_knapsack mixed_binary general_linear

Submitter Variables Constraints Density Status Group Objective MPS File
Cézar Augusto Nascimento e Silva 9258 203455 3.25106e-04 open graphdraw 72118.5* graphdraw-grafo2.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 9258 9258
Constraints 203455 203455
Binaries 8844 8844
Integers 134 134
Continuous 280 280
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.000325106 0.000325106
Nonzeroes 612366 612366
Constraint Classification Properties
Original Presolved
Total 203455 203455
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 0 0
Variable Bound 341 341
Set Partitioning 2211 2211
Set Packing 0 0
Set Covering 0 0
Cardinality 0 0
Invariant Knapsack 191620 191620
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 0
Integer Knapsack 0 0
Mixed Binary 147 147
General Linear 9136 9136
Indicator 0 0


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

value min median mean max
Components 0.4771212
Constraint % 49.3367 49.3367 49.3367 49.3367
Variable % 49.2763 49.2763 49.2763 49.2763
Score 0.5005080

Best Known Solution(s)

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

## Warning in lapply(df["exactobjval"], as.numeric): NAs introduced by coercion
ID Objective Exact Int. Viol Cons. Viol Obj. Viol Submitter Date Description
4 72118.5 72118.5 1e-07 1e-07 0 Edward Rothberg 2020-04-22 Obtained with Gurobi 9.0 using the solution improvement heuristic
3 73377.0 72616.5 0e+00 0e+00 0 Frederic Didier 2020-01-22 Obtained with Google OR-tools using 8 Threads through generating subproblems by fixing part of the current solution and trying to solve them with a sub CP-SAT solver
2 95024.5 0e+00 0e+00 0 Robert Ashford and Alkis Vazacopoulus 2019-12-18 Found with ODH|CPLEX
1 230722.5 230722.5 0e+00 0e+00 0 - 2018-10-13 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to graphdraw-grafo2 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-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-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
neos-3402294-bobin easy 2904 2616 0 288 591076 2034888 Jeff Linderoth neos-pseudoapplication-71 0.06724999999999949 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 19685.99997550038 benchmark benchmark_suitable variable_bound set_partitioning invariant_knapsack mixed_binary general_linear
neos-3695882-vesdre open 6135 5955 0 180 191504 598115 Hans Mittelmann neos-pseudoapplication-71 518.3505480226543* decomposition variable_bound set_partitioning cardinality invariant_knapsack 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}

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