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 and writes it to stdout. 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 ROWS COLS [OPTION]...

Options:

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

Formats for matrices: dense, sparse

Network Matrices

The executable cmr-generate-network creates a random \( m \)-by- \(n\) network matrix, either ternary (default) or binary and writes it to stdout. 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 ROWS COLS [OPTION]...

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; default: dense.

Formats for matrices: dense, sparse

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 \( p \) and writes it to stdout. It can be called as follows, where \( m \) equals ROWS and \( n \) equals COLS.

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

Options:

-o FORMAT Format of output; default: dense.

Formats for matrices: dense, sparse

Random Perturbations

The executable cmr-perturb-random copies the matrix from file IN-MAT to the file OUT-MAT after applying random perturbations. It can be called as follows.

./cmr-perturb-random IN-MAT OUT-MAT [OPTION]...

Options:

-i FORMAT Format of file IN-MAT; default: dense.
-o FORMAT Format of file OUT-MAT; default: same as format of IN-MAT.
-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.

Formats for matrices: dense, sparse If IN-MAT is -, then the input matrix is read from stdin. If OUT-MAT is -, then the output matrix is written to stdout.

Wheel Matrices

The executable cmr-generate-wheel creates an \( n \)-by- \( n \) wheel matrix \( W_n \) or a variant \( W'_n \) and writes it to stdout.

\[ W_n = \begin{pmatrix} 1 & 1 & 0 & 0 & 0 & \dots & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 & \dots & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & \dots & 0 & 0 \\ \vdots & & & \ddots & \ddots & & & \vdots \\ \vdots & & & & \ddots & \ddots & & \vdots \\ 0 & 0 & \dots & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & \dots & 0 & 0 & 0 & 1 & 1 \\ 1 & 0 & \dots & 0 & 0 & 0 & 0 & 1 \end{pmatrix}, \qquad \qquad \qquad W'_n = \begin{pmatrix} 1 & 1 & 0 & \color{red}{1} & \color{red}{1} & \dots & \color{red}{1} & \color{red}{1} \\ 0 & 1 & 1 & \color{red}{1} & \color{red}{1} & \dots & \color{red}{1} & \color{red}{1} \\ 0 & 0 & 1 & 1 & 0 & \dots & 0 & 0 \\ \vdots & & & \ddots & \ddots & & & \vdots \\ \vdots & & & & \ddots & \ddots & & \vdots \\ 0 & 0 & \dots & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & \dots & 0 & 0 & 0 & 1 & 1 \\ 1 & 0 & \dots & 0 & 0 & 0 & 0 & 1 \end{pmatrix} \]

It can be called as follows, where \( n \) equals ORDER.

./cmr-generate-wheel ORDER [OPTION]...

Options:

-01 In each column with two 0s in rows 1 and 2, replace them by 1s; default: off
-o FORMAT Format of output; default: dense.

Formats for matrices: dense, sparse

Note: The matrices \( W_n \) are graphic for all \( n \). The modified matrices \( W'_n \) for odd \( n \) are minimally non-totally unimodular, which means that the matrix itself has determinant \( |\det W'_n| = 2 \), but all of its proper submatrices are totally unimodular.

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 and writes it to stdout. 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 MIPFILE [OPTION]...

Options:

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

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