Submitter | Variables | Constraints | Density | Status | Group | Objective | MPS File |
---|---|---|---|---|---|---|---|
Stephan Beyer | 3379 | 20538 | 1.04584e-03 | open | genus | -21* | genus-sym-grafo5708-48.mps.gz |
Minimum Genus instance of grafo5708.48 from the Rome Graphs, with symmetry-breaking constraints.
Detailed explanation of the following tables can be found here.
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 |
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 |
Available nonzero structure and decomposition information. Further information can be found here.
Decomposed structure of original problem (dec-file)
Decomposed structure after trivial presolving (dec-file)
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 |
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 |
---|---|---|---|---|---|---|---|---|
3 | -21 | 0 | 0 | 0 | Edward Rothberg | 2019-12-13 | Obtained with Gurobi 9.0 | |
2 | -19 | 0 | 0 | 0 | Robert Ashford and Alkis Vazacopoulus | 2019-12-18 | Found using ODH|CPlex | |
1 | -15 | 0 | 0 | 0 | - | 2018-10-12 | Solution found during MIPLIB2017 problem selection. |
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.
@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}
}