variable_bound set_partitioning invariant_knapsack mixed_binary general_linear

Submitter Variables Constraints Density Status Group Objective MPS File
Cézar Augusto Nascimento e Silva 2050 20661 1.47208e-03 open graphdraw 39852.99999999995* graphdraw-mainerd.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 2050 2050
Constraints 20661 20661
Binaries 1860 1860
Integers 62 62
Continuous 128 128
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.00147208 0.00147208
Nonzeroes 62350 62350
Constraint Classification Properties
Original Presolved
Total 20661 20661
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 0 0
Variable Bound 157 157
Set Partitioning 465 465
Set Packing 0 0
Set Covering 0 0
Cardinality 0 0
Invariant Knapsack 17980 17980
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 0
Integer Knapsack 0 0
Mixed Binary 67 67
General Linear 1992 1992
Indicator 0 0


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

value min median mean max
Components 0.4771212
Constraint % 48.3326 48.3326 48.3326 48.3326
Variable % 48.4878 48.4878 48.4878 48.4878
Score 0.4979440

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 39853 0 0e+00 0 Edward Rothberg 2020-04-22 Obtained with Gurobi 9.0 using the solution improvement heuristic
3 44372 0 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 49016 0 0e+00 0 Robert Ashford and Alkis Vazacopoulus 2019-12-18 Found using ODH|CPlex
1 49949 0 3e-07 0 - 2018-10-13 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to graphdraw-mainerd 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-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
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-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
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


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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