sorrell4

binary variable_bound

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Toni Sorrell	2048	504451	9.76562e-04	hard	independentset	-24	sorrell4.mps.gz

These instances are based on Neil Sloane’s Challenge problems: Independent Sets in Graphs.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	2048	2048
Constraints	504451	504451
Binaries	2048	2048
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000976562	0.000976562
Nonzeroes	1008900	1008900

Constraint Classification Properties
	Original	Presolved
Total	504451	504451
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	504451	504451
Set Partitioning	0	0
Set Packing	0	0
Set Covering	0	0
Cardinality	0	0
Invariant Knapsack	0	0
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	0.30103
Constraint %		100	100	100	100
Variable %		100	100	100	100
Score	0.00000

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	Exact	Submitter	Date	Description
3	-24	-24	Jan Krüger	2023-08-20	Solution as found on https://oeis.org/A265032/a265032.html, reported optimal by Pablo San Segundo
2	-24		Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
1	-23	-23	-	2018-10-11	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to sorrell4 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	Constraints	Nonz.	Submitter	Group	Objective	Tags
sorrell3	easy	1024	1024	0	169162	338324	Toni Sorrell	independentset	-16	benchmark binary benchmark_suitable variable_bound
z26	open	17937	17937	0	850513	1715613	Daniel Bienstock	–	-1195.0*	binary variable_bound set_packing
sorrell7	open	2048	2048	0	78848	157696	Toni Sorrell	independentset	-198.0*	binary variable_bound
sorrell8	easy	2046	2046	0	18944	37888	Toni Sorrell	independentset	-350	binary decomposition variable_bound
manna81	easy	3321	18	3303	6480	12960	MIPLIB submission pool	–	-13164	variable_bound

Reference

No bibliographic information available