graphdraw-grafo2

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.

Location of instance in collection

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

Structure

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

Nonzero entries of original problem

Nonzero entries after trivial presolving

Decomposed structure of original problem (dec-file)

Decomposed structure after trivial presolving (dec-file)

	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	Submitter	Date	Description
4	72118.5	72118.5	1e-07	1e-07	Edward Rothberg	2020-04-22	Obtained with Gurobi 9.0 using the solution improvement heuristic
3	73377.0	72616.5	0e+00	0e+00	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	Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found with ODH\|CPLEX
1	230722.5	230722.5	0e+00	0e+00	-	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

Reference

@article{ESILVA2017207,
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 = {http://dx.doi.org/10.1016/j.endm.2017.03.027},
author = {Cézar Augusto N. e Silva and Haroldo Gambini Santos}
}