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steiner covering problems
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lperron authored and acco32 committed Dec 22, 2017
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51 changes: 51 additions & 0 deletions examples/data/scp/README.steiner_triple.txt
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STEINER TRIPLE COVERING PROBLEM test instances

Let n = number of variables
m = number of triples
T(i) = set of 3 indices of i-th triple

The problem is;

MIN \sum_{j=1]^n x_j

SUBJ. TO:

\sum_{j \in T(i)} x_j \geq 1, for i = 1,...,m,

x_j \in {0,1} for all j = 1,...,n




The following files are in the distribution:

FILE : INSTANCE : n : m
............................................
data.9 : stn9 : 9 : 12
data.15 : stn15 : 15 : 35
data.27 : stn27 : 27 : 117
data.45 : stn45 : 45 : 330
data.81 : stn81 : 81 : 1080
data.135 : stn135 : 135 : 3015
data.243 : stn243 : 243 : 9801
data.405 : stn405 : 405 : 27270
data.729 : stn729 : 729 : 88452

The file format is:

Line 1: n m
Lines 2 to m+1: 3 variable indices for triple


Best known solutions

stn9 : 5 optimal (Fulkerson et al., 1974)
stn15 : 9 optimal (Fulkerson et al., 1974)
stn27 : 18 optimal (Fulkerson et al., 1974)
stn45 : 30 optimal (Ratliff, 1979)
stn81 : 61 optimal (Mannino and Sassano, 1995)
stn135 : 103 optimal (Ostrowski et al., 2009, 2010)
stn243 : 198 optimal (Ostrowski et al., 2009, 2010)
stn405 : 335 BKS (Resende & Toso, 2010)
stn729 : 617 BKS (Resende & Toso, 2010)

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