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 -20* 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.

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.

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.

ID Objective Exact Int. Viol Cons. Viol Obj. Viol Submitter Date Description
1 -20 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-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 -26* 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 -15* 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 2372590 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}
}

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