1 Overview Among hard combinatorial optimization problems there is an increasing body of special cases known in which optimal solutions can be obtained eeciently. These special cases may be expressed as constraints on graph structure, such as chordal or interval graphs 4, 6] which allow linear-time solution of problems like vertex coloring, or Monge matrix edge weights which allow eecient solut...

When expanding a filtration with stochastic process it is easily possible for semimartingale no longer to remain in the enlarged filtration. Y. Kchia and P. Protter indicated way avoid this pitfall 2015, but they were unable give decomposition except special cases. We provide compute such decomposition, moreover we sufficient condition Itô processes (Corollary 3.7). This can be interpreted term...