graph40-20-1rand

binary decomposition precedence set_partitioning invariant_knapsack

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Michael Bastubbe	31243	99067	1.11645e-04	open	graphs	-15*	graph40-20-1rand.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	31243	31086
Constraints	99067	95770
Binaries	31243	31086
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000111645	0.000111800
Nonzeroes	345557	332840

Constraint Classification Properties
	Original	Presolved
Total	99067	95770
Empty	0	0
Free	0	0
Singleton	157	0
Aggregations	0	0
Precedence	0	3140
Variable Bound	0	0
Set Partitioning	157	157
Set Packing	0	0
Set Covering	49298	0
Cardinality	0	0
Invariant Knapsack	49455	92473
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	2.198657
Constraint %		0.635899	0.635899	0.635899	0.635899
Variable %		0.633726	0.633726	0.633726	0.633726
Score	0.992034

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	Int. Viol	Cons. Viol	Obj. Viol	Submitter	Date	Description
2	-15		0	0	0	Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	-14	-14	0	0	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to graph40-20-1rand 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
graph40-40-1rand	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
graph20-20-1rand	easy	2183	2183	5587	19277	Michael Bastubbe	graphs	-9	benchmark binary decomposition benchmark_suitable 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}
}