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 -15* genus-sym-grafo5708-48.mps.gz

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

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.

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.

ID Objective Exact Int. Viol Cons. Viol Obj. Viol Submitter Date Description
1 -15 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-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 -20* precedence set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear
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
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 -19* 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}
}

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