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A new method for fast optimum wavelength assignments (WLA) within two fiber optical transparent WDM rings is proposed. The combinatorial WLA problem is solved optimally by a heuristic. The generalized shortest path routing matrix (GM) is used and its decomposition in 4 areas significantly simplifies the global WLA by a fast sequential algorithm. This algorithm is less complex and its calculation time is far below the time needed for other heuristics, e.g. one order of magnitude faster than the cyclic shift method. A second compact WLA algorithm that is based on formulas is proposed. The complexity of its implementation reduces to less than 15 lines of code. This algorithm supports either local WLAs with the time complexity O(1) per demand pair or global WLAs for WDM rings of F facility nodes with O(F2).