genus-sym-grafo5708-48

precedence set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Stephan Beyer	3379	20538	1.04584e-03	open	genus	-21*	genus-sym-grafo5708-48.mps.gz

Minimum Genus instance of grafo5708.48 from the Rome Graphs, with symmetry-breaking constraints.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	3379	3378
Constraints	20538	20538
Binaries	3377	3377
Integers	1	1
Continuous	1	0
Implicit Integers	0	0
Fixed Variables	1	0
Nonzero Density	0.00104584	0.00104615
Nonzeroes	72579	72579

Constraint Classification Properties
	Original	Presolved
Total	20538	20538
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	26	26
Variable Bound	0	0
Set Partitioning	246	246
Set Packing	0	0
Set Covering	5604	420
Cardinality	810	810
Invariant Knapsack	13824	19008
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	27
Integer Knapsack	0	0
Mixed Binary	27	0
General Linear	1	1
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	1.633468
Constraint %		0.0294031	0.131264	0.147016	0.245026
Variable %		0.3552400	2.369670	3.374780	3.374780
Score	0.053673

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	Submitter	Date	Description
3	-21	Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
2	-19	Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	-15	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to genus-sym-grafo5708-48 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
genus-sym-g62-2	open	12912	12910	1	1	78472	275855	Stephan Beyer	genus	-38.0*	precedence set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear
genus-g61-25	open	14380	14378	1	1	94735	332877	Stephan Beyer	genus	-40.0*	numerics set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear
neos-950242	easy	5760	5520	240	0	34224	104160	NEOS Server Submission	neos-pseudoapplication-72	4	benchmark benchmark_suitable aggregations precedence variable_bound set_partitioning set_covering invariant_knapsack general_linear
supportcase10	hard	14770	14770	0	0	165684	555082	Michael Winkler	–	7	benchmark binary benchmark_suitable aggregations precedence variable_bound set_covering invariant_knapsack
genus-sym-g31-8	open	3484	3482	1	1	32073	401199	Stephan Beyer	genus	-23.0*	numerics precedence set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear

Reference

@inproceedings{BCHK16,
 author    = {Stephan Beyer and Markus Chimani and Ivo Hedtke and Michal Kotrbc{\'{\i}}k},
 title     = {{A} {Practical} {Method} for the {Minimum} {Genus} of a {Graph}: {Models} and {Experiments}},
 booktitle = {Experimental Algorithms---Proceedings 15th {SEA} 2016, St. Petersburg},
 editor    = {Andrew V. Goldberg and Alexander S. Kulikov},
 pages     = {75--88},
 year      = {2016},
 series    = {LNCS},
 volume    = {9685},
 publisher = {Springer},
 doi       = {10.1007/978-3-319-38851-9_6}
}

@article{DBLP:journals/comgeo/WelzlBGLTTV97,
author    = {Giuseppe {Di Battista} and Ashim Garg and Giuseppe Liotta and Roberto Tamassia and Emanuele Tassinari and Francesco Vargiu},
title     = {An Experimental Comparison of Four Graph Drawing Algorithms},
journal   = {Comput. Geom.},
volume    = {7},
pages     = {303--325},
year      = {1997},
url       = {https://doi.org/10.1016/S0925-7721(96)00005-3},
doi       = {10.1016/S0925-7721(96)00005-3}
}