# LOP (linear ordering problem) instances

The instances presented here use Mersenne Twister (available at
http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html) to generate
edge costs randomly from the integers in the interval [1,99]. Their
densities (probability that an edge between any two vertices exists)
vary from 1% to 100%. Instances are separated by size (number of
vertices n), and named as follows:
n[number of vertices]d[density]-[instance ID].
There are five instances for each combination of size and density. The
format of the instances is as follows:
[number of vertices n]
c_{11} c_{12} c_{13} ... c_{1n}
c_{21} c_{22} c_{23} ... c_{2n}
. . .
c_{n1} c_{n2} c_{n3} ... c_{nn}
where "c_{uv}" is the cost of edge (u,v).
instances with n = 500 (zip file)
instances with n = 1000 (zip file)
instances with n = 2000 (zip file)
instances with n = 3000 (zip file)
instances with n = 4000 (zip file)
instances with n = 8000 (zip file)
These instances are used in:
C.S. Sakuraba and M. Yagiura, Efficient local search algorithms for
the linear ordering problem, International Transactions in Operational
Research, 17 (2010) 711-737.

**
Mutsunori YAGIURA**