linear programming - Ford-Falkerson's algorithm for undirected graphs (What am I missing?) -

i "found" algorithm finding maximum flow in undirected graph think isn't correct, can't find mistake. here algorithm: construct new directed graph in following way: every edge ${u,v}$ create edges $(u,v)$ , $(v,u)$ $c((u,v))=c((v,u))=c({u,v})$. apply ford-falkerson's algorithm on new graph. make flow in our first graph in following way: let's $f((u,v))\ge f((v,u))$, direct edge ${u,v}$ $u$ $v$ , take $f'((u,v))=f((u,v))-f((v,u))$. maximum flow our undirected graph, because otherwise construct flow corresponding directed graph, contradiction. reason think have missed there article on internet problem , don't think wrote article such trivial problem.

and article: http://www.inf.ufpr.br/pos/techreport/rt_dinf003_2004.pdf

thanks!

ford-fulkerson not best algorithm find maximum flow in directed graph, , in undirected case possible better (close linear-time if recall correctly).

you don't cite article talking about, describe algorithm better yours.

for many problems in optimization, not difficult find algorithm gives optimal solution; nevertheless there lot of work find efficient ones.