v150d30-2hopcds

binary variable_bound set_covering

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Austin Buchanan	150	7822	8.86312e-02	hard	2hopcds	41.0	v150d30-2hopcds.mps.gz

A problem in wireless networks. The objective is to select a minimum number of relay nodes so that any two nonadjacent nodes can communicate by way of the chosen relay nodes in at most s hops, where s is a problem input. The 2-hop case of this problem can be formulated as a set cover/hitting set problem with n binary variables and n^2 constraints: _{ k N(i) N(j) } x_k for nonadjacent node pairs {i,j}. Despite the formulation’s simplicity, instances with as few as 120 variables are left unsolved after one hour using Gurobi 7.0.2.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	150	148
Constraints	7822	6228
Binaries	150	148
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.0886312	0.0883098
Nonzeroes	103991	81399

Constraint Classification Properties
	Original	Presolved
Total	7822	6228
Empty	0	0
Free	0	0
Singleton	2	0
Aggregations	0	0
Precedence	0	0
Variable Bound	4	4
Set Partitioning	0	0
Set Packing	0	0
Set Covering	7816	6224
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	0.301030
Constraint %		100.0000	100.0000	100.0000	100.0000
Variable %		98.6667	98.6667	98.6667	98.6667
Score	0.013333

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
2	41	41	0	0	0	Ishibashi Yasumi	2020-08-28	Solved with NuOpt using 16 threads within 60 hours
1	41	41	0	0	0	-	2018-10-10	Solution found during MIPLIB2017 problem selection

Similar instances in collection

The following instances are most similar to v150d30-2hopcds 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
glass-sc	easy	214	214	6119	63918	Marc Pfetsch	maxfeassub	23	benchmark binary benchmark_suitable set_covering
iis-glass-cov	easy	214	214	5375	56133	Marc Pfetsch	iis	20.99999999999999	binary benchmark_suitable set_covering
iis-hc-cov	easy	297	297	9727	142971	Marc Pfetsch	iis	17	binary benchmark_suitable set_covering
seymour	easy	1372	1372	4944	33549	W. Cook, P. Seymour	–	423	benchmark binary benchmark_suitable variable_bound set_covering
ramos3	open	2187	2187	2187	32805	F. Ramos	–	186.0*	binary set_covering

Reference

@UNPUBLISHED{buchanan2017,
  author = {Buchanan, Austin and Validi, Hamidreza},
  title = {The optimal design of low-latency virtual backbones},
  note = {Manuscript in preparation},
  year = {2017}
}