genus-sym-g31-8

numerics precedence set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Stephan Beyer	3484	32073	3.59039e-03	open	genus	-21*	genus-sym-g31-8.mps.gz

Minimum Genus instance, with symmetry breaking constraints, of g.31.8 (undirected) of the AT&T Graphs by Stephen C. North.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	3484	3483
Constraints	32073	32073
Binaries	3482	3482
Integers	1	1
Continuous	1	0
Implicit Integers	0	0
Fixed Variables	1	0
Nonzero Density	0.00359039	0.00359142
Nonzeroes	401199	401199

Constraint Classification Properties
	Original	Presolved
Total	32073	32073
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	26	26
Variable Bound	0	0
Set Partitioning	234	234
Set Packing	0	0
Set Covering	14532	8376
Cardinality	837	837
Invariant Knapsack	16416	22572
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	1.612784
Constraint %		0.0436504	0.720232	0.0966545	25.5355
Variable %		0.3445310	2.486360	3.3304600	4.4789
Score	0.275756

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
2	-21		0	0	0	Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	-19		0	0	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to genus-sym-g31-8 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-g31-8	open	3484	3482	1	1	32047	401147	Stephan Beyer	genus	-23*	numerics set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear
genus-sym-grafo5708-48	open	3379	3377	1	1	20538	72579	Stephan Beyer	genus	-21*	precedence set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear
graph20-80-1rand	hard	16263	16263	0	0	55107	191997	Michael Bastubbe	graphs	-6	binary decomposition precedence set_partitioning invariant_knapsack
genus-sym-g62-2	open	12912	12910	1	1	78472	275855	Stephan Beyer	genus	-34.0*	precedence set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear
graph40-20-1rand	open	31243	31243	0	0	99067	345557	Michael Bastubbe	graphs	-15*	binary decomposition precedence set_partitioning invariant_knapsack

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}
}