genus-sym-g62-2

precedence set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Stephan Beyer	12912	78472	2.72253e-04	open	genus	-38.0*	genus-sym-g62-2.mps.gz

Minimum Genus instance, with symmetry breaking constraints, of g.62.2 (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	12912	12911
Constraints	78472	78472
Binaries	12910	12910
Integers	1	1
Continuous	1	0
Implicit Integers	0	0
Fixed Variables	1	0
Nonzero Density	0.000272253	0.000272274
Nonzeroes	275855	275855

Constraint Classification Properties
	Original	Presolved
Total	78472	78472
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	53	53
Variable Bound	0	0
Set Partitioning	516	516
Set Packing	0	0
Set Covering	18880	736
Cardinality	3240	3240
Invariant Knapsack	55728	73872
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	54
Integer Knapsack	0	0
Mixed Binary	54	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	1.939519
Constraint %		0.007670	0.0548497	0.076742	0.076742
Variable %		0.092944	1.1553200	1.765940	1.765940
Score	0.046430

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	Submitter	Date	Description
5	-38		Peng Lin, Mengchuan Zou, Shaowei Cai	2024-01-23	Computed the local search solver Local-MIP (https://github.com/shaowei-cai-group/Local-MIP) by Peng Lin, Mengchuan Zou, and Shaowei Cai.
4	-34	1e+100	Edward Rothberg	2020-09-14	Found with Gurobi
3	-30	1e+100	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	-28		Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	-20		-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to genus-sym-g62-2 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-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
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
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
neos-3230376-yser	easy	57000	56976	0	24	786916	2372592	Jeff Linderoth	neos-pseudoapplication-4	Unbounded	precedence variable_bound set_partitioning set_covering invariant_knapsack mixed_binary

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}
}