Modeling the cardiac conduction system is a challenging problem in the context of computational cardiac electrophysiology. Its ventricular section, the Purkinje system, is responsible for triggering tissue electrical activation at discrete terminal locations, which subsequently spreads throughout the ventricles. In this paper, we present an algorithm that is capable of estimating the location of the Purkinje system triggering points from a set of random measurements on tissue. We present the properties and the performance of the algorithm under controlled synthetic scenarios. Results show that the method is capable of locating most of the triggering points in scenarios with a fair ratio between terminals and measurements. When the ratio is low, the method can locate the terminals with major impact in the overall activation map. Mean absolute errors obtained indicate that solutions provided by the algorithm are useful to accurately simulate a complete patient ventricular activation map.