Extended relaxation method, including dynamic programming

The authors propose a method called the extended relaxation matching method (ERM), which is an extension of ordinary relaxation matching. It is shown that dynamic programming (DP) matching can be characterized as a special case of the extended method. The DP matching method is transformed into the equivalent form called product-type DP matching. Using this equivalent form, the relation between the ERM and the DP matching is discussed. By the representation of the DP matching as a special case of the ERM, it is shown that the recurrence formula, which forms the core in the DP matching process, corresponds to the procedure contained in common to the algorithm in ERM. Moreover, a new matching method which can be obtained by changing the variables is introduced