tanglegram4

binary benchmark_suitable set_covering invariant_knapsack

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Falk Hueffner	56048	110404	5.35255e-05	easy	huefner	10696	tanglegram4.mps.gz

The NP-hard Balanced Subgraph problem (variant of MaxCut) encoded as ILPs. Real-world instances from two applications from bioinformatics, finding monotone subsystems in gene regulatory networks (https://dx.doi.org/10.1007/s10878-009-9212-2) and finding optimal layouts of tanglegrams (https://dx.doi.org/10.1007/978-3-642-11269-0). Imported from the MIPLIB2010 submissions.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	56048	56048
Constraints	110404	110404
Binaries	56048	56048
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	5.35255e-05	5.35255e-05
Nonzeroes	331212	331212

Constraint Classification Properties
	Original	Presolved
Total	110404	110404
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	0	0
Set Partitioning	0	0
Set Packing	0	0
Set Covering	84761	25643
Cardinality	0	0
Invariant Knapsack	25643	84761
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	0	0
General Linear	0	0
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	1.079181
Constraint %		0.000906	2.11150	0.00181	23.193
Variable %		0.005350	4.20305	0.00892	46.123
Score	0.125292

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	10696	10696	0	0	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to tanglegram4 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	Continuous	Constraints	Nonz.	Submitter	Group	Objective	Tags
tanglegram6	easy	9182	9182	0	17712	53136	Falk Hueffner	huefner	1224	binary benchmark_suitable set_covering invariant_knapsack
toll-like	easy	2883	2883	0	4408	13224	Falk Hueffner	huefner	610	binary benchmark_suitable set_covering invariant_knapsack
vpphard2	easy	199999	199999	0	198450	648340	C. Cardonha	–	81	binary decomposition benchmark_suitable set_partitioning cardinality invariant_knapsack
vpphard	easy	51471	51471	0	47280	372305	C. Cardonha	–	5	binary decomposition benchmark_suitable set_partitioning cardinality invariant_knapsack
30_70_45_095_100	easy	10976	10975	1	12526	46640	J. Walser	30_70	3	binary decomposition benchmark_suitable precedence variable_bound set_covering mixed_binary

Reference

No bibliographic information available