# v150d30-2hopcds

### binaryvariable_boundset_covering

Submitter Variables Constraints Density Status Group Objective MPS File
Austin Buchanan 150 7822 8.86312e-02 open 2hopcds 41* 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 1 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.

# 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.

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)

No solution available for v150d30-2hopcds .

# 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 Integers Continuous Constraints Nonz. Submitter Group Objective Tags
glass-sc easy 214 214 0 0 6119 63918 Marc Pfetsch maxfeassub 23 benchmark binary benchmark_suitable set_covering
iis-glass-cov easy 214 214 0 0 5375 56133 Marc Pfetsch iis 21 binary benchmark_suitable set_covering
iis-hc-cov easy 297 297 0 0 9727 142971 Marc Pfetsch iis 17 binary benchmark_suitable set_covering
seymour easy 1372 1372 0 0 4944 33549 W. Cook, P. Seymour 423 benchmark binary benchmark_suitable variable_bound set_covering
ramos3 open 2187 2187 0 0 2187 32805 F. Ramos 192.0* 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}
}

Last Update Jun 24, 2020 by Gabriel Kressin
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