SSDs(Solid State Drives) have many attractive features such as high performance, low power consumption, shock resistance, and low weight, so they replace HDDs to a certain extent. An SSD has FTL(Flash Translation Layer) which emulate block storage devices like HDDs. A garbage collection, one of major functions of FTL, effects highly on the performance and the lifetime of SSDs. However, there is no de facto standard for new garbage collection algorithms. To solve this problem, we propose trace driven offline optimal algorithms for garbage collection of FTL. The proposed algorithm always guarantees minimal number of erase operation. In addition, we verify our proposed algorithm using TPC trace.