With the development of passive optical networks, the fiberwireless (FiWi) network is envisioned to be a promising network architecture for supporting the centralized cloud computing (CCC) and mobile edge computing (MEC) simultaneously. However, existing work that focuses on collaborative computation offloading (CCO) based on FiWi network, aims at minimizing the energy consumption of mobile devices, and ignores the demands of high realtime tasks. Therefore, regarding high realtime tasks, we present a centralized cloud and edge cloud collaborative computation offloading problem, which aims to minimize the total processing time of the computation tasks, as well as its formalized description. It proves to be NPhard by reducing it to a bin packing problem, and the offloading strategy with shortest time will be selected. Two algorithms are proposed as our solutions, i.e., a heuristic collaborative computation offloading algorithm (HCCOA) and a genetic algorithm for collaborative computation offloading (GA4CCO). The HCCOA chooses the strategy with the shortest time via comparing the total processing time among different computation offloading strategies. And the GA4CCO is to get an optimal or suboptimal strategy. Experimental results show that the HCCOA and GA4CCO can reduce the total processing time of the obtained task offloading  strategy by 4.34% and 18.41% on average, respectively. In addition, the GA4CCO can reduce the total processing time of the obtained task offloading strategy by 14.49% in comparison to the HCCOA.