graph20-20-1rand

benchmark binary decomposition benchmark_suitable precedence set_partitioning invariant_knapsack

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Michael Bastubbe	2183	5587	1.58055e-03	easy	graphs	-9	graph20-20-1rand.mps.gz

Packing Cuts in Undirected Graphs. Instances are described in 4.1.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	2183	2146
Constraints	5587	5180
Binaries	2183	2146
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.00158055	0.00159766
Nonzeroes	19277	17760

Constraint Classification Properties
	Original	Presolved
Total	5587	5180
Empty	0	0
Free	0	0
Singleton	37	0
Aggregations	0	0
Precedence	0	370
Variable Bound	0	0
Set Partitioning	37	37
Set Packing	0	0
Set Covering	2738	0
Cardinality	0	0
Invariant Knapsack	2775	4773
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	1.579784
Constraint %		2.6834	2.6834	2.6834	2.6834
Variable %		2.6561	2.6561	2.6561	2.6561
Score	0.966486

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	-9	-9	0	0	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to graph20-20-1rand 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	Constraints	Nonz.	Submitter	Group	Objective	Tags
graph20-80-1rand	hard	16263	16263	55107	191997	Michael Bastubbe	graphs	-6	binary decomposition precedence set_partitioning invariant_knapsack
graph40-20-1rand	open	31243	31243	99067	345557	Michael Bastubbe	graphs	-15*	binary decomposition precedence set_partitioning invariant_knapsack
graph40-40-1rand	open	102600	102600	360900	1260900	Michael Bastubbe	graphs	-9*	binary precedence set_partitioning invariant_knapsack
graph40-80-1rand	open	283648	283648	1050112	3671552	Michael Bastubbe	graphs	-7*	binary precedence set_partitioning invariant_knapsack
neos-3555904-turama	easy	37461	37461	146493	793605	Hans Mittelmann	neos-pseudoapplication-81	-34.7	benchmark binary benchmark_suitable aggregations precedence variable_bound set_partitioning set_packing cardinality invariant_knapsack

Reference

@article{or:BergnerLuebbeckeWitt:16,
   Author   = {
M. Bergner and M.E. L\"{u}bbecke and J.T. Witt},
   Title    = {A Branch-Price-and-Cut Algorithm for Packing Cuts in Undirected Graphs},
   Journal  = {Journal of Experimental Algorithmics (JEA)},
   Year     = {2016},
   Volume   = {21 },
   Number   = {2016--},
   Pages    = {Article No. 1.2},
   Month   = {Jan},
   Publisher    = {ACM New York, NY, USA},
   DOI      = {10.1145/2851492}
}