RankWidthApproximate

This program was written for the master's thesis A simulated annealing method for computing rank-width. It implements a simulated annealing based algorithm for approximating rank-width, F4-rank-width and maximum matching-width, and outputs the corresponding decomposition in dot graph format. The program was tested on both Windows and Linux, and can make use of SIMD instructions (AVX2 recommended) and multiple cores.

Usage

RankWidthApproximate.exe [options] graph.dgf

The following options are available:

-ac Enables adaptive cooling.
-d Approximate the F4-rank-width of a directed input graph (can not be used in combination with -mm).
-d2u Approximate the rank-width or maximum matching-width of a directed input graph by first converting it to undirected (each arc becomes an undirected edge).
-is seed Sets the seed for the random generator for the initial solution (by default the same random generator is used as for the search process).
-mm Approximate the maximum matching-width of an undirected input graph (or directed converted to undirected with -d2u).
-s seed Sets the seed for the random generator (random by default).
-t temperature Sets the initial temperature (default is 5.0).
-td delta Enables the thresholding heuristic with the given threshold delta.
-tl seconds Stops the search process if it is still running after the given number of seconds (the search process also stops when the temperature drops below 0.05).
-v Output more information during the search process.

Input graph format

The program supports a number of variations of the text based DIMACS graph format, for both undirected and directed graphs.

Undirected

For undirected graphs the following rules apply:

Lines starting with c, n or x are ignored.
Before any edges are defined, a header is expected in the following format:
```
p format vtxCount edgeCount
```
The format field is ignored by the program, but usually contains the word edge. A file should only have a single header line.
Edges can be defined as either
```
vtxId1 vtxId2
```
or
```
e vtxId1 vtxId2
```
for an edge between vtxId1 and vtxId2. There are expected to be as many edge definitions as specified in the header. In case of the e format, any other input after vtxId2 is ignored.
Vertex ids can be anything without spaces. As such it does not matter if vertices are numbered from 0, from 1 or identified with any other number, letter or label.

Some examples of valid inputs:

c 5 vertex cycle
p edge 5 5
e 0 1
e 1 2
e 2 3
e 3 4
e 0 4

x low 19.00
p edge 3 3
n 92 1.00
n 26 1.00
n 93 1.00
e 26 93
e 26 92
e 92 93

p edge 7 11
e A B
e A C
e B D
e B E
e C D
e D F
e D E
e D G
e C G
e E F
e F G

Directed

For directed graphs the format is mostly similar to the undirected format, except that the header now contains the number of arcs instead of the number of edges, and the way the arcs are defined differs slightly from the way edges were defined. They are defined as either

vtxId1 vtxId2

a vtxId1 vtxId2

for an arc from vtxId1 to vtxId2. In case of the a format, any other input after vtxId2 (such as weights) is ignored.

Tests

Some unit tests are provided that verify some parts of the program.

Build flags

There are some build flags that can be enabled to have extra logging:

LOG_PROGRESS At the end, print when the first decomposition of each width was found
CACHE_HISTOGRAM At the end, print a (textual) histogram of cache hit rates per iteration

Citing

When using this program for research work, please cite my thesis as follows:

@MastersThesis{nouwt2022rankwidth,
    title = {A simulated annealing method for computing rank-width},
    author = {Nouwt, Florian},
    year = {2022},
    month = May,
    school = {Utrecht University},
    url = {https://doi.org/20.500.12932/41566}
}

Gericom / RankWidthApproximate