The library comes with several instance generators. However, they are disabled for compilation by default, and can be enabled by adding

-DGENERATORS=on

to the cmake call. In the following we provide details for each of these generators.

Graphic Matrices

The executable cmr-generate-graphic creates a random \( m \)-by- \(n\) matrix that is graphic. To this end, it first constructs a spanning tree with \( m+1 \) nodes by subsequently connecting each new leaf to one of the previously created nodes. The new edge then indexes a row of the matrix. Second, \( n \) random pairs of distinct nodes are generated that are then connected by a new edge indexed by a column. The matrix is the representation matrix of the final graph with respect to the spanning tree. It can be called as follows, where \( m \) equals ROWS and \( n \) equals COLS.

./cmr-generate-graphic [OPTIONS] ROWS COLS

Options:

-B NUM Benchmarks the recognition algorithm for the created matrix with NUM repetitions.
-o FORMAT Format of output FILE; default: dense.

Formats for matrices are dense-matrix, sparse-matrix.

Network Matrices

The executable cmr-generate-network creates a random \( m \)-by- \(n\) network matrix, either ternary (default) or binary. In order to generate a ternary matrix, it first constructs a random graphic matrix (see above) and then modifies its signs via Camion's Signing Algorithm. For the binary matrix, a random spanning tree is constructed and oriented to become an arborescence with root. For the co-tree edges, only node pairs are considered, where the second node lies on the directed path from the first node to the root. It can be called as follows, where \( m \) equals ROWS and \( n \) equals COLS.

./cmr-generate-network [OPTIONS] ROWS COLS

Options:

-b Restrict to binary network matrices based on arborescences.
-B NUM Benchmarks the recognition algorithm for the created matrix with NUM repetitions.
-o FORMAT Format of output FILE; default: dense.

Formats for matrices are dense-matrix, sparse-matrix.

Random Matrices

The executable cmr-generate-random creates a random \( m \)-by- \(n\) binary matrix whose entries are chosen uniformly at random with a given probability \( p \). It can be called as follows, where \( m \) equals ROWS and \( n \) equals COLS.

./cmr-generate-random [OPTIONS] ROWS COLS p

Options:

-o FORMAT Format of output FILE; default: dense.

Formats for matrices are dense-matrix, sparse-matrix.

Random Perturbations

The executable cmr-perturb-random modifies a matrix by applying a specified number of random perturbations of different types. It can be called as follows.

./cmr-perturb-random [OPTIONS] MATRIX

Options:

-i FORMAT Format of input MATRIX file; default: dense.
-o FORMAT Format of output matrix; default: same as input format.
-0 NUM Turn NUM randomly chosen nonzero entries to 0s.
-1 NUM Turn NUM randomly chosen zero entries into 1s.
--1 NUM Turn NUM randomly chosen zero entries into -1s.
-b NUM Flip NUM randomly chosen entries over the binary field.
-t NUM Flip NUM randomly chosen entries over the ternary field.

If MATRIX is -, then the matrix will be read from stdin. Formats for matrices are dense-matrix, sparse-matrix.

Gurobi Coefficient Matrix

The executable cmr-extract-gurobi extracts the coefficient matrix of a mixed-integer program file that can be read by the Gurobi solver. Building it requires that Gurobi is found by cmake. To this end, you may need to set the cmake option -DGUROBI_DIR to your Gurobi installation directory. It can be called as follows.

./cmr-extract-gurobi [OPTIONS] MIPFILE

Options:

-o FORMAT Format of output matrix; default: dense.

Formats for matrices are dense-matrix, sparse-matrix. MIPFILE must refer to a file that Gurobi can read.