This is a implementation of a half-approximation algorithm, b-Suitor, for computing a b-Matching of maximum weight in a graph with weights on the edges. b-Matching is a generalization of the well-known Matching problem in graphs, where the objective is to choose a subset of M edges in the graph such that at most a specified number b(v) of edges in M are incident on each vertex v. Subject to this restriction we maximize the sum of the weights of the edges in M.

CITATION:

Khan, A., Pothen, A., Mostofa Ali Patwary, M., Satish, N. R., Sundaram, N., Manne, F., & Dubey, P. (2016). Efficient approximation algorithms for weighted b-matching. SIAM Journal on Scientific Computing, 38(5), S593-S619.

CONTACT:

Arif Khan, [email protected] Alex Pothen, [email protected] Mahantesh Halappanavar, [email protected]

TO COMPILE:

Make

INPUT:

The implementation accepts two inputs: i) a graph G in MATRIX MARKET FORMAT (.mtx) and ii) EITHER a file that has n lines where n is the number of vertices in G. The i th lines contains a single integer representing the b value of i th vertex, i.e., b[i] value. OR a constant b for all vertices. if b=0 then the code generates b-value for each vertex v, randomly between 1 and sqrt(d(v)), where d(v) is the degree of v.

OUTPUT:

For each vertex v, a priority queue holds the final matching. The user are requested look into bMatching.h for the priority queue data structure, called NODE. An example of the implementation is included in the main function in bMatching.cpp.

HELP:

./bMatching -h

will show the input argument for the code as follows:

Usage: -f -e -b -a -v -g

    -f problemname  : file containing graph. Currently inputs .mtx files
    -e bfilename    : Optional input. (currently not implemented)
    -b bval         : constant b value if b=0 then randomly generated.
    -a algorithm    : Algorithm 0:unsorted 1:partial sorted mode (defualt)
    -t              : bipartite graph 
    -v              : verbose

TEST EXAMPLE:

A test problem named Ga10As10H30, a quantum chemistry problem, from Florida Matrix Collection has been included with the codes. To experiment with the problem with constant b value = 2, the user can issue the following command:

./bMatching -f turon_m.mtx -b 2 -v

THE CORRECT OUTPUT: Graph (189924, 778531) Reading Done....!! took 1.35321 bValue is constant for each vertex Input Processing Done: 0.010898 Initialization Done...!! Start Matching189924 Iteration: 1 54135 0.004274 Iteration: 2 19842 0.00208 Iteration: 3 6572 0.001006 Iteration: 4 1703 0.000416 Iteration: 5 533 0.000182 Iteration: 6 93 0.000154 Iteration: 7 41 0.000203 Iteration: 8 13 0.000167 Iteration: 9 4 0.000136 Iteration: 10 1 0.000168 Iteration: 11 1 0.000108 Iteration: 12 0 0.000106 Matching Done....!! Iterations: 12 Initialization Time: 0.006812 Matching Time: 0.009305 Total Time: 0.016117 Matching Weight: 109378 General Matching Verified..!!

The Iteration lines specifies how many vertices to be processed after that iteration and how much time it took for that iteration. The user can also run the same experiment without the -v command which will generate less information.

Graph (189924, 778531) Reading Done....!! took 1.28027 bValue is constant for each vertex Input Processing Done: 0.010949 Initialization Done...!! Start Matching189924 Matching Done....!! Total Matching Time: 0.015312