cyclepath-classifier 0.2.1

A command-line tool for automatically calculating round complexity of LCL problems in cycles and paths based on their description in the node-edge-checkable formalism

Cyclepath classifier

A command-line tool for automatically calculating round complexity of LCL problems in cycles and paths based on their description in the node-edge-checkable formalism. It also reports the number of solvable/unsolvable instances of a problem when classifying it (see examples below).

The tool is based on the techniques described in this paper.

Requirements

• Python 3.8.3 or later version

Getting started

Run the tool specifying node and edge constraints of a problem in the node-edge-checkable formalism.

The required parameters are -t or --type, -n or --node-constr and -e or --edge-constr. There are also optional parameters specifying start and end constraints: --start-constr and --end-constr

--type accepts 3 values: dir, undir and tree for directed cyclepath, undirected cyclepath and a rooted tree respectively.

Unless the type is tree, the tool will assume that the problem is defined for a path if either --start-constr or --end-constr is specified. Otherwise, cycle setting is assumed.

Examples

$ python3 -m cyclepath_classifier -t undir -n "{ 11, 22, 33 }" -e "{ 12, 21, 13, 31, 23, 32 }"

Round complexity of the problem is Θ(log* n)
There are infinitely many solvable instances
There are finitely many unsolvable instances

$ python3 -m cyclepath_classifier -t undir -n "{ 12, 21 }" -e "{ 11, 22 }"

Round complexity of the problem is Θ(n)
There are infinitely many solvable instances
There are infinitely many unsolvable instances

$ python3 -m cyclepath_classifier -t undir -n "{00, 1M}" -e "{01, 10, 11, MM}" --start-constr "{ 1 }" --end-constr "{ 1 }"

A problem cannot be of 'undirected' type if its constraints are asymmetric. Otherwise it is not well-defined.

$ python3 -m cyclepath_classifier -t dir -n "{00, 1M}" -e "{01, 10, 11, MM}" --start-constr "{ 1 }" --end-constr "{ 1 }"

Round complexity of the problem is O(1)
There are finitely many solvable instances
There are infinitely many unsolvable instances

$ python3 -m cyclepath_classifier -t tree -e "{ 11, 22 }"

Round complexity of the problem is O(1)
There are infinitely many solvable instances
There are finitely many unsolvable instances

python3 -m cyclepath_classifier -t tree -e "{ 12, 13, 23, 21, 31, 32 }"
Round complexity of the problem is Θ(log* n)
There are infinitely many solvable instances
There are finitely many unsolvable instances

Tests

Run tests with python -m unittest discover. See the tests/test.py file for details.