[VUT FIT 2020] FLP (Functional and Logic programming) project no. 2

Assignment: Finding all spanning trees of undirected graphs in Prolog

Dependencies

• swipl (SWI-Prolog)

Usage

Simply compile with make and run the program as follows:

./flp20-log < input
    input       input file containing a graph in valid format.
                Invalid edges, duplicates and self loop edges are ignored

Input graph fomat

Program expects an input where each line contains a single edge with the following notation:

<V1> <V2>\n
<V3> <V4>\n
<V5> <V6>\n
...

where each V marks a single vertex and is a single character from [A-Z]. Trailing whitespace characters preceding newline character are ignored.

Output spanning tree fomat

Each output line describes a single spanning tree with the following notation:

<V1>-<V2> <V3>-<V4> ... <Vn-1>-<Vn>\n
...

where each pair <Vi>-<Vj> denotes an edge in the spanning tree.

The program will terminate without any output if the input is invalid or the input graph contains no spanning trees (due to various reasons such as with disconnected graphs).

Example

<<
A B
A C
A D
>>
A-B A-C A-D

Implementation

The solution is based on mathematical properties of graphs and spanning trees. A spanning tree must contain all graph verticies and no cycles (it is a tree after all). As such, a spanning tree will contain exactly |V| - 1 edges because with less than |V| - 1 edges we cannot possibly connect all |V| graph vertices in a tree and with more than |V| - 1 edges a cycle will naturally occur.

The program thus works as follows:

1. Input is parsed into a list of edges [(A,B), (C,D), ...] of size K.
2. All possible combinations of edges with size |V|-1 are generated from the list (no duplicate edges).
3. Candidate solutions are filtered out with a simple check as candiate solution (edge combination) must contain all graph vertices.
4. Each candidate is traversed with depth first search and is selected as a valid spanning tree if all graph verticies were visited. DFS checks for connectivity as a candidate of size |V| - 1 with V verticies does not have to be a spanning tree. Such subgraph will be disconnected and contain a cycle.

Tests

No automated tests were created, however './tests' directory contains few valid example inputs with expected reference outputs.

Apart from that, previously existing test script was used to test the core functionality and various edge cases

Authors

• Ondřej Pavela