## Functions

On our webpage, we provide solvers for different kinds of problems. The functions, that are currently implemented, are described below.

### BiqBin

##### Description

Computes the solution of a binary quadratic problem subject to linear constraints.

min x'Fx + c'x s.t. Ax = b, x in {0,1}^n

##### Input

The parameters A,b,c, and F defining problem (refer to above) in a sparse format, where F is symmetric, thus we report only the upper (or lower) triangular part.

Example of an input:

3 2

A

1 1 1

1 2 1

1 3 1

b

1 1

F

1 1 1

1 3 2

2 2 2

3 3 3

c

2 1

3 2

The first line contains the number of variables n and the number of constraints m.

The next lines define the parameters.

There is line A, and the following lines denote the elements of A in a sparse format (row, column, value).

There is line b, and the following lines denote the elements of b in a sparse format (row, value).

There is line F, and the following lines denote the elements of the upper triangular part of the symmetric matrix F in sparse format (row, column, value).

There is line c, and the following lines denote the elements of c in a sparse format (row, value).

##### Output

A file with the result and info about process' execution on HPC.

##### Source code

### Max-Cut

##### Description

Computes max-cut in a given graph.

##### Input

A graph in the edge list file. Example of format:

7 9

1 2 46

2 3 -22

3 4 76

4 5 -180

5 6 22

6 7 -50

7 1 14

1 5 61

3 7 3

The first line contains the number of vertices n and the number of edges m. The next m lines contain three integers denoting edges and their weights.

##### Output

A file with the result and info about running on HPC.

##### Source code

### Stable set

##### Description

Computes the maximum stable set in a given unweighted graph.

##### Input

A graph in the edge list file. Example of format:

7 9

1 2 1

2 3 1

3 4 1

4 5 1

5 6 1

6 7 1

7 1 1

1 5 1

3 7 1

The first line contains the number of vertices n and the number of edges m. The next m lines contain three integers denoting edges and their weights.

##### Output

A file with the result and info about running on HPC.