GitHub - vamsik83/weighted-matching: Given a weighted bipartite graph G =(U,V,E) and a non-negative cost function C = cij associated with each edge (i,j)∈E, the problem of finding a match M ⊂ E such that minimizes ∑ cpq|(p,q) ∈ M, is a very important problem this problem is a classic example of Combinatorial Optimization, where a optimization problem is solved iteratively by solving an underlying combinatorial problem. This problem is also known as the assignment problem. The techniques developed in the Hungarian method assumes that the representation of the underlying bipartite graph is dense and thus emphasizes on the asymptotic complexity of computing the shortest augmenting path which is O((|V|+|U| +|E|)log(|V|+|U|)). However in practice this worst case asymptotic bound was never hit especially in case of the sparse representation of the underlying bipartite graph. In practice we found that the runtime (cputime) of the algorithm is dominated by the time to update the dual variables rather than the time to compute the shortest augmenting path. In the original algorithm techniques to update the dual variables are ignored totally and hence the updating of the dual variables need an asymptotic time of O(|U|+|V|+|E|) , in this work we update the dual variables only in O(|V|+|U|) thus improving the performance of solving the assignment problem by a great extent. We encountered this problem in the context of building efficient numerically stable linear solvers which solve equations of the form Ax = b. It has been an accepted fact that permuting the matrix A so that the elements along the diagonal of A are large is a desired property. Weighted bipartite graph matching is used extensively to permute the row/column's of the matrix A so that its closely diagonally dominant.

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Given a weighted bipartite graph G =(U,V,E) and a non-negative cost function C = cij associated with each edge (i,j)∈E, the problem of finding a match M ⊂ E such that minimizes ∑ cpq|(p,q) ∈ M, is a very important problem this problem is a classic example of Combinatorial Optimization, where a optimization problem is solved ite…

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Name		Name	Last commit message	Last commit date
Latest commit History 4 Commits
.deps		.deps
CVS		CVS
PerlScripts		PerlScripts
myutil		myutil
Bipartite.cpp		Bipartite.cpp
Bipartite.h		Bipartite.h
Bipartite.hpp		Bipartite.hpp
Bipartite2.cpp		Bipartite2.cpp
Bipartite_C.c		Bipartite_C.c
Bipartite_bcup.c		Bipartite_bcup.c
Bipartite_bcup.h		Bipartite_bcup.h
CompareAbs.c		CompareAbs.c
CreateMC64PermFile.c		CreateMC64PermFile.c
DoubleHeap.c		DoubleHeap.c
FloatingFormat.c		FloatingFormat.c
Heap.c		Heap.c
Heap.h		Heap.h
InPerm.txt		InPerm.txt
LogTest.c		LogTest.c
MC64Driver.c		MC64Driver.c
Makefile		Makefile
Makefile.Build.Solaris		Makefile.Build.Solaris
Makefile.gmake		Makefile.gmake
Makefile.windows		Makefile.windows
MeasureTime.c		MeasureTime.c
MeasureTime.h		MeasureTime.h
README		README
ReadSparse.c		ReadSparse.c
ValidatePermutation.c		ValidatePermutation.c
create_perm		create_perm
dump_tran_matrices.pl		dump_tran_matrices.pl
fdiff		fdiff
gmon.out		gmon.out
inplace_permute		inplace_permute
intel_mc64		intel_mc64
mc64		mc64
mc64.diag		mc64.diag
mc64.h		mc64.h
mc64.out		mc64.out
mc64_program		mc64_program
mm2rc.pl		mm2rc.pl
molex.out		molex.out
pre.solaris.c		pre.solaris.c
run_ufl_tests.pl		run_ufl_tests.pl
ticks.txt		ticks.txt
times.linux32.log		times.linux32.log
win_bug.cpp		win_bug.cpp

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This directory contains the implementation of a weighted matching algorithm.


BUILDING:

To build on a 64-bit machine run: "make -f Makefile PF=x84_64", to build on other platforms see the corresponding Makefiles. This should generate an 
executable named "bipartite1-linux64". To build on MAC just use "make -f Makefile PF=x84_64" (make sure you have g++ and XCode installed).

RUNNING:

The program reads a sparse matrix representation of the weighted bipartite graph, the sparse matrix should be in a "Row Compressed Format". Now you 
can run the program "./bipartite1-linux64 {sparse_matrix.txt}"

Questions:

Email: Vamsi Kundeti (vamsi.krishnak@gmail.com)