sheshang / Feedback-Vertex-Set

#FVS_BF

This implementation of Feedback vertex Set problem with Brute force approach is to understand the improvement done by parameterized version (https://github.com/feldsherov/pace2016/) implemented by Svyatoslav Feldsherov (Moscow State University) in the PACE2016 challange (https://pacechallenge.wordpress.com/pace-2016/track-b-feedback-vertex-set/).

#Input:
    list of edges
#Output:
    list of vertices in minimum feedback vertex set

#Algorithm:
    Store all the edges in edgestore
    For each combination of vertex-set (in increasing order of size):
        reduce the graph by removing all edges adjecent to the selected combination subset
        check acyclicity of that reduced graph with help of union-find algorithm
        if reduced graph is acyclic
            the current combination of vertex set is the minimum vertex set.
            return that subset and terminate program

#Running Time:
    Let say input has E edges and V vertices,
    Graph reading takes O(E) time.
    For subset creation O(2^N) time. O(V^k) is time for k-sub algorithm and V is for all possibility of length of set
        In isAcyclic() function:
            copy making of edgelist takes O(E) time
            cyclicity checking takes O(E*log(V)) time. (for each edge in edgelist copy, verify by union find algorithm)

So total time complexity will be O(2^N*E*log(V))

Here we used union-find algorithm by path compression and by rank, so it gives the better time then original O(V) time logic.

#put your all testcases in 'testcases' folder with '*.graph' format.

#give permission to buil.sh and run.sh on your computer by following command.
    chmod +x build.sh
    chmod +x run.sh

#now build program with,
    ./build.sh

#to run you have two options
    if you want to run only sigle testcase, comment second script block in run.sh as shown there, and on terminal type,
    ./run.sh filename.graph

    if you want to run multiple testcases automatically, comment first option there, uncomment second script block and on terminal type,
    ./run.sh
    
To execute ipynb files you need two output files. One will be created with running this code and another one you have to generate with the implementation you want to compare with.

Testcases has been generated by me and some testcases taken from the PACE2016 site.