genus-g61-25

numerics set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Stephan Beyer	14380	94735	2.44351e-04	open	genus	-40.0*	genus-g61-25.mps.gz

Minimum Genus instance of g.61.25 (undirected) of the AT&T Graphs by Stephen C. North. Best solution was obtained with Optimization Direct Heuristic, which basically is an add on working with CPLEX directly through callbacks to generate additional heuristic solutions

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	14380	14379
Constraints	94735	94735
Binaries	14378	14378
Integers	1	1
Continuous	1	0
Implicit Integers	0	0
Fixed Variables	1	0
Nonzero Density	0.000244351	0.000244368
Nonzeroes	332877	332877

Constraint Classification Properties
	Original	Presolved
Total	94735	94735
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	0	0
Set Partitioning	540	540
Set Packing	0	0
Set Covering	20592	1104
Cardinality	3480	3480
Invariant Knapsack	70064	89552
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	58
Integer Knapsack	0	0
Mixed Binary	58	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	1.959041
Constraint %		0.006350	0.0503601	0.0635385	0.118605
Variable %		0.083455	1.1043900	1.6412800	1.641280
Score	0.044701

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	-40	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.
2	-34	Ed Klotz	2019-09-26	Obtained with Optimization Direct Heuristic, which basically is an add on working with CPLEX directly through callbacks to generate additional heuristic solutions
1	-26	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to genus-g61-25 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-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}
}