Monitoring heart diseases often requires frequent measurements of electrocardiogram (ECG) signals at different periods of the day, and at different situations (e.g., traveling, and exercising). This can only be implemented using mobile devices in order to cope with mobility of patients under monitoring, thus supporting continuous monitoring practices. However, these devices are energy-aware, have limited computing resources (e.g., CPU speed and memory), and might lose network connectivity, which makes it very challenging to maintain a continuity of the monitoring episode. In this paper, we propose a mobile monitoring solution to cope with these challenges by compromising on the fly resources availability, battery level, and network intermittence. In order to solve this problem, first we divide the whole process into several subtasks such that each subtask can be executed sequentially either in the server or in the mobile or in parallel in both devices. Then, we developed a mathematical model that considers all the constraints and finds a dynamic programing solution to obtain the best execution path (i.e., which substep should be done where). The solution guarantees an optimum execution time, while considering device battery availability, execution and transmission time, and network availability. We conducted a series of experiments to evaluate our proposed approach using some key monitoring tasks starting from preprocessing to classification and prediction. The results we have obtained proved that our approach gives the best (lowest) running time for any combination of factors including processing speed, input size, and network bandwidth. Compared to several greedy but nonoptimal solutions, the execution time of our approach was at least 10 times faster and consumed 90% less energy.