graphdraw-gemcutter

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.

Location of instance in collection

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

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 %		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

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}
}